THE       ORIGIN 
OF      SPECTRA 

.     BY 

PAUL  D.  FOOTE 

Physicist,  U.  S.  Bureau  of  Standards 
AND 

F.  L.  MOHLER 

Physicist,  U.  S.  Bureau  of  Standards 


American  Chemical  Society 
Monograph  Series 


BOOK    DEPARTMENT 
The  CHEMICAL  CATALOG  COMPANY  Inc. 

19  EAST  24ra  STREET,  NEW  YORK,  U.  S.  A. 
1922 


f 


COPYRIGHT,  1922,  BY 
The  CHEMICAL  CATALOG  COMPANY,  Inc. 

All  Rights* Reserved 


Press  of 

J.  J.  Little  &  Ives  Company 
New  York,  U.  S.  A. 


GENERAL   INTRODUCTION 

American    Chemical    Society    Series    of 
Scientific  and  Technologic  Monographs 

By  arrangement  with  the  Interallied  Conference  of  Pure  and  Applied 
Chemistry,  which  met  in  London  and  Brussels  in  July,  1919,  the  Ameri- 
can Chemical  Society  was  to  undertake  the  production  and  publication 
of  Scientific  and  Technologic  Monographs  on  chemical  subjects.  At  the 
same  time  it  was  agreed  that  the  National  Research  Council,  in  coopera- 
tion with  the  American  Chemical  Society  and  the  American  Physical 
Society,  should  undertake  the  production  and  publication  of  Critical 
Tables  of  Chemical  and  Physical  Constants.  The  American  Chemical 
Society  and  the  National  Research  Council  mutually  agreed  to  care  for 
these  two  fields  of  chemical  development.  The  American  Chemical 
Society  named  as  Trustees,  to  make  the  necessary  arrangements  for  the 
publication  of  the  monographs,  Charles  L.  Parsons,  Secretary  of  the 
American  Chemical  Society,  Washington,  D.  C.;  John  E.  Teeple,  Treas- 
urer of  the  American  Chemical  Society,  New  York  City;  and  Professor 
Gellert  Alleman  of  Swarthmore  College.  The  Trustees  have  arranged 
for  the  publication  of  the  American  Chemical  Society  series  of  (a) 
Scientific  and  (b)  Technologic  Monographs  by  the  Chemical  Catalog 
Company  of  New  York  City. 

The  Council,  acting  through  the  Committee  on  National  Policy  of 
the  American  Chemical  Society,  appointed  the  editors,  named  at  the  close 
of  this  introduction,  to  have  charge  of  securing  authors,  and  of  consider- 
ing critically  the  manuscripts  prepared.  The  editors  of  each  series  will 
endeavor  to  select  topics  which  are  of  current  interest  and  authors  who 
are  recognized  as  authorities  in  their  respective  fields.  The  list  of  mono- 
graphs thus  far  secured  appears  in  the  publisher's  own  announcement 
elsewhere  in  this  volume. 

The  development  of  knowledge  in  all  branches  of  science,  and  espe- 
cially in  chemistry,  has  been  so  rapid  during  the  last  fifty  years  and 
the  fields  covered  by  this  development  have  been  so  varied  that  it  is 

3 


4  GENERAL  INTRODUCTION 

difficult  for  any  individual  to  keep  in  touch  with  the  progress  in  branches 
of  science  outside  his  own  specialty.  In  spite  of  the  facilities  for  the 
examination  of  the  literature  given  by  Chemical  Abstracts  and  such 
compendia  as  Beilstein's  Handbuch  der  Organischen  Chemie,  Richter's 
Lexikon,  Ostwald's  Lehrbuch  der  Allgemeinen  Chemie,  Abegg's  and 
Gmelin-Kraut's  Handbuch  der  Anorganischen  Chemie  and  the  English 
and  French  Dictionaries  of  Chemistry,  it  often  takes  a  great  deal  of 
time  to  coordinate  the  knowledge  available  upon  a  single  topic.  Con- 
sequently when  men  who  have  spent  years  in  the  study  of  important 
subjects  are  willing  to  coordinate  their  knowledge  and  present  it  in  con- 
cise, readable  form,  they  perform  a  service  of  the  highest  value  to  their 
fellow  chemists. 

It  was  with  a  clear  recognition  of  the.  usefulness  of  reviews  of  this 
character  that  a  Committee  of  the  American  Chemical  Society  recom- 
mended the  publication  of  the  two  series  of  monographs  under  the  aus- 
pices of  the  Society. 

Two  rather  distinct  purposes  are  to  be  served  by  these  monographs. 
The  first  purpose,  whose  fulfilment  will  probably  render  to  chemists  in 
general  the  most  important  service,  is*  to  present  the  knowledge  available 
upon  the  chosen  topic  in  a  readable  form,  intelligible  to  those  whose 
activities  may  be  along  a  wholly  different  line.  Many  chemists  fail  to 
realize  how  closely  their  investigations  may  be  connected  with  other  work 
which  on  the  surface  appears  far  afield  from  their  own.  These  mono- 
graphs will  enable  such  men  to  form  closer  contact  with  the  work  of 
chemists  in  other  lines  of  research.  The  second  purpose  is  to  promote 
research  in  the  branch  of  science  covered  by  the  monograph,  by  furnish- 
ing a  well  digested  survey  of  the  progress  already  made  in  that  field  and 
by  pointing  out  directions  in  which  investigation  needs  to  be  extended. 
To  facilitate  the  attainment  of  this  purpose,  it  is  intended  to  include 
extended  references  to  the  literature,  which  will  enable  anyone  interested 
to  follow  up  the  subject  in  more  detail.  If  the  literature  is  so  voluminous 
that  a  complete  bibliography  is  impracticable,  a  critical  selection  will  be 
made  of  those  papers  which  are  most  important. 

The  publication  of  these  books  marks  a  distinct  departure  in  the 
policy  of  the  American  Chemical  Society  inasmuch  as  it  is  a  serious 
attempt  to  found  an  American  chemical  literature  without  primary 
regard  to  commercial  considerations.  The  success  of  the  venture  will 
depend  in  large  part  upon  the  measure  of  cooperation  which  can  be 
secured  in  the  preparation  of  books  dealing  adequately  with  topics  of 
general  interest;  it  is  earnestly  hoped,  therefore,  that  every  member  of 


GENERAL  INTRODUCTION  5 

the  Various  organizations  in  the  chemical  and  allied  industries  will  recog- 
nize the  importance  of  the  enterprise  and  take  sufficient  interest  to 
justify  it. 

AMERICAN    CHEMICAL    SOCIETY 

BOARD   OF   EDITORS 

Scientific  Series:—  Technologic  Series:— 

WILLIAM  A.  NOTES,  Editor,  JOHN  JOHNSTON,  Editor, 

GILBERT  N.  LEWIS,  C.  G.  DERICK, 

LAFAYETTE  B.  MENDEL,  WILLIAM  HOSKINS, 

ARTHUR  A.  NOTES,  F.  A.  LIDBURT, 

JULIUS  STIEGLITZ.  ARTHUR  D.  LITTLE, 

C.  L.  REESE, 
C.  P.  TOWNSEND. 


American  Chemical  Society 

MONOGRAPH    SERIES 

Other  monographs  in  the  series  of  which  this  book  is  a  part  now 
ready  or  in  process  of  being  printed  or  written. 

Organic  Compounds  of  Mercury. 

By  Frank  C.  Whitmore.     397  pages.     Price  $4.50. 
Industrial  Hydrogen. 

By  Hugh  S.  Taylor.     210  pages.     Price  $3.50. 
The  Chemistry  of  Enzyme  Actions. 

By  K.  George  Falk.     140  pages.     Price  $2.50. 
The  Vitamins. 

By  H.  C.  Sherman  and  S.  L.  Smith.     273  pages.     Price  $4.00. 
The  Chemical  Effects  of  Alpha  Particles  and  Electrons. 

By  Samuel  CT  Lind.     180  pages.     Price  $3.00. 
Zirconium  and  Its  Compounds. 

By  F.  P.  Venable.     Price  $2.50. 
The  Properties  of  Electrically  Conducting  Systems. 

By  Charles  A.  Kraus.     Price  $4.50. 
Carotinoids  and  Related  Pigments:   The  Chromolipoids. 

By  Leroy  S.  Palmer.    About  200  pages,  illustrated. 
Thyroxin.     By  E.  C.  Kendall. 

The  Properties  of  Silica  and  the  Silicates.     By  Robert  B.  Sosman. 
Coal  Carbonization.     By  Horace  C.  Porter. 
The  Corrosion  of  Alloys.     By  C.  G.  Fink. 
Piezo-Chemistry.     By  L.  H.  Adams. 
Cyanamide.     By  Joseph  M.  Braham. 
Ammonia  Compounds.     By  E.  C.  Franklin. 
Wood  Distillation.     By  L.  F.  Hawley. 
Solubility.     By  Joel  H.  Hildebrand. 
Glue  and  Gelatin.     By  Jerome  Alexander. 
Organic  Arsenical  Compounds.    By  George  W.  Raiziss.     Jos.  L. 

Gavron. 
Valence,  and  the  Structure  of  Atoms  and  Molecules.     By  Gilbert 

N.  Lewis. 

Shah  Oil.    By  Ralph  H.  McKee. 

Aluminothermic  Reduction  of  Metals.     By  B.  D.  Saklatwalla. 
The  Analysis  of  Rubber.     By  John  B.  Tuttle. 
The  Chemistry  of  Leather  Manufacture.     By  John  A.  Wilson. 
Absorption  Carbon.     By  N.  K.  Chancy. 
Refining  Petroleum.     By  George  A.  Burrell,  et  al. 
Extraction  of  Gasoline  from  Natural  Gas.     By  George  A.  Burrell. 

The  CHEMICAL  CATALOG  COMPANY,  Inc. 

19   EAST   24TH   STREET,   NEW   YORK,   U.    S.   A. 


PREFACE 

Although  several  accounts  of  the  quantum  theory  of  spectra  from 
the  mathematical  standpoint  have  appeared  in  the  past  year,  the  experi- 
mental aspect  of  the  problem  has  been  greatly  subordinated. 

In  this  book  the  authors  have  endeavored  to  present  the  subject 
from  the  experimental  side.  However,  in  order  to  do  this,  it  was  found 
necessary  to  briefly  discuss  the  theoretical  developments.  In  this 
regard,  the  important  assumptions  involved  are  enumerated,  and  only 
the  essential  steps  in  the  mathematical  analysis  are  presented.  The 
reader  will  find  the  detailed  mathematical  treatment  in  the  papers 
given  as  references,  especially  in  the  works  of  Bohr  and  Sommerfeld. 

The  experimental  phase  of  the  quantum  hypothesis  as  applied  to 
spectroscopy  was  given  its  first  impetus  by  the  pioneer  work  of  J. 
Franck  whose  later  important  researches  have  contributed  much  to 
the  development  of  the  subject.  The  theoretical  deductions  of  Sommer- 
feld on  fine  structure  have  been  beautifully  verified  by  the  precision 
spectroscopic  work  of  Paschen.  The  most  recent  contributions  of  Bohr 
on  atomic  structure  have  removed  many  of  the  objections  of  the  chemist 
to  the  physicist's  conception  of  a  planetary  structure  with  revolving 
electrons.  At  the  same  time  Bohr's  viewpoint  has  necessitated  the  re- 
vision of  some  of  the  conceptions  of  the  physicist. 

The  subject  matter  is  recognizedly  in  a  transitional  stage  and  the 
theoretical  interpretation  of  experimental  phenomena  here  given  is  in 
no  sense  complete  or  final.  However,  the  experimental  facts  will  remain 
and  no  time  is  more  opportune  for  their  systematic  correlation  than  the 
present  moment. 

This  book  is  incomplete  in  many  respects.  For  example,  consider- 
ation of  the  extensive  experiments  on  the  Stark  and  Zeeman  effects  and 
on  band  spectra  has  been  omitted,  in  part  because  their  adequate  treat- 
ment seemed  to  require  more  space  than  was  deemed  advisable  to  devote 
to  these  subjects,  and  in  part  because  of  the  authors'  inexperience  in  these 
fields  of  spectroscopy. 

7 


8  PREFACE 

The  title  of  the  book  was  suggested  by  a  lecture  of  Prof.  J.  C.  McLen- 
nan whose  many  experiments  in  this  field  of  physics  are  considered  in 
the  text. 

The  authors  desire  to  acknowledge  the  helpful  cooperation  and 
advice  of  their  colleague  Dr.  W.  F.  Meggers.  Many  of  their  "experi- 
ments have  been  undertaken  with  Dr.  Meggers  as  co-worker  and  he  has 
very  kindly  prepared  most  of  the  photographic  prints  of  spectra  repro- 
duced here  as  half-tones.  Dr.  K.  T.  Compton  furnished  the  advance 
manuscript  of  his  paper  on  Cumulative  lonization,  a  synopsis  of  which 
is  given  in  Chapter  VI.  Dr.  R.  C.  Tolman,  Dr.  C.  A.  Skinner  and  Mr. 
Arthur  E.  Ruark  have  very  generously  given  much  of  their  time  in 
reading  the  manuscript,  and  have  offered  many  suggestions  which  have 
been  incorporated  in  the  text. 

The  authors  wish  to  express  their  appreciation  of  the  interest  with 
which  the  late  Dr.  C.  W.  Waidner,  former  Chief  of  the  Heat  Division 
of  this  Bureau,  followed  the  course  of  their  work  until  within  a  few  days 
of  his  death.  The  authors  also  desire  to  thank  Dr.  S.  W.  Stratton  for 
placing  at  their  disposal  every  means  and  facility  which  could  advance 
their  own  experimental  work  in  this  subject.  And  finally,  the  authors 
are  especially  grateful  to  the  Monograph  Committee  of  the  American 
Chemical  Society,  its  Chairman,  Prof.  W.  A.  Noyes,  and  Prof.  A.  A. 
Noyjs,  for  making  possible  the  publication  of  this  volume. 

P.  D.  F. 

Bureau  of  Standards,  May  22,  1922.  F.  L.  M. 


TITLES  OF  CHAPTERS 

CHAPTER  PAGE 

I.  THE  QUANTUM  THEORY  OF  SPECTROSCOPY   ....  15 
II.  ENERGY  DIAGRAMS 51 

III.  lONIZATION   AND    RESONANCE    POTENTIALS    FOR   THE    ELE- 

MENTS   60 

IV.  LINE  ABSORPTION  SPECTRA  OF  ATOMS 78 

V.    LINE  EMISSION  SPECTRA  OF  ATOMS 109 

VI.     CUMULATIVE  IONIZATION 148 

VII.     THERMAL  EXCITATION 157 

VIII.     THERMOCHEMICAL  RELATIONS      ........  177 

IX.     X-RAY  SPECTRA 192 

X.     PHOTO-ELECTRIC  EFFECT  IN  VAPORS 216 

XI.    DETERMINATIONS  OF  h  INVOLVING  LINE  SPECTRA     .      .  223 

APPENDICES 

APPENDIX 

I.     COMPUTATIONAL  DATA 227 

PERIODIC  TABLE 231 

II.  BOHR'S  THEORY  OF  ATOMIC  STRUCTURE 232 

INDEX  OF  SUBJECTS 243 

INDEX  OF  AUTHORS  249 


TABLE  OF  CONTENTS 

HAPTEK 

I.    THE  QUANTUM  THEORY  OF  SPECTROSCOPY      .      .      .     .15 

The  Simple  Theory  of  Hydrogen  and  Ionized  Helium    .  16 
Ratio  of  Mass  of  Hydrogen  Nucleus  and  Hydrogen 

Atom  to  Mass  of  Electron,  and  Value  of  elm     .      .  18 

Elliptical  Orbits 19 

Relativity  of  Mass 24 

The  Principle  of  Selection .  26 

Experimental  Verification  by  Fine  Structure  Analysis.  27 

Atoms  with  Many  Electrons 30 

Derivation  of  the  Ritz  Equation 32 

Application  of  the  Ritz  Equation .34 

Fine  Structure,  Doublets  and  Triplets 37 

Nuclear  Defect  of  a  Ring  of  Electrons 37 

Spark  Spectra '.......  39 

Spectroscopic  Tables 43 

X-Rays           46 

II.    ENERGY  DIAGRAMS 51 

III.  lONIZATION   AND    RESONANCE    POTENTIALS    FOR   THE    ELE- 

MENTS          60 

Group  I 63 

Group  1 1 63 

Group  III 63 

Group  IV,  Group  V .  65 

Group  VI 66 

Group  VII,  Groups  VIII  and  0 67 

Hydrogen 68 

The  Normal  Helium  Atom         ........  69 

The  Hydrogen  Molecule •  74 

IV.  LINE  ABSORPTION  SPECTRA  OF  ATOMS        78 

Line  Absorption  Spectra  of  Normal  Atoms    ....  78 

Reversed  Lines 82 

Resonance  Radiation 86 

The  Broadening  of  Spectral  Lines 91 

Doppler  Effect 91 

Impact  Damping 92 

Line  Absorption  Spectra  of  Excited  Atoms    ....  93 

The  Measurement  of  r  (the  life  of  an  excited  atom)       .  93 

Absorption  of  Subordinate  Series  Lines 97 

11 


12  CONTENTS 

CHAPTER  PAGE 

V.     LINE  EMISSION  SPECTRA  OF  ATOMS 109 

Metals  of  Group  II  of  the  Periodic  Table       ....  118 

Relation  between  1  @  and  1  S        124 

Metals  of  Group  I  of  the  Periodic  Table 127 

The  Rare  Gases 133 

Helium 133 

Neon 136 

Franck  and  Einsporn's  Observations  onMercury     .      .  137 
Quantitative  Spectroscopic  Analysis  in  its  Relation  to 

the  Origin  of  Spectra 141 

Long  Lines 141 

Raies  Ultimes 141 

VI.    CUMULATIVE  IONIZATION •    .     .     .     .  V.  148 

Excitation  by  Electronic  Impact '.  149 

Excitation  by  Absorption  of  Radiation     .      .      .      .      .  150 

Numerical  Magnitudes 152 

Arcs  below  the  lonization  Potential 153 

lonization   by   Successive   Photo-Electric   Action  .      .  154 

Further  Conclusions       • 155 

VII.     THERMAL  EXCITATION 157 

Thermodynamic  Considerations 157 

Simple  lonization ;  159 

Double  lonization •    .      .      .      .      .  161 

Thermal  Excitation  without  lonization 163 

Flame  Spectra 165 

Spectral  Lines  Correlated  with  Temperature       .      .      .  169 

Solar  Spectra 170 

Stellar  Spectra 172 

VIII.  THERMOCHEMICAL  RELATIONS 177 

Electron  Affinity  of  Atoms 177 

Grating  Energy,  lonization  Potential  and  Electron 

Affinity 179 

lonization  of  Vapors  of  Compounds 184 

Critical  Potentials  and  Radiation  from  Elements  in  the 

Polyatomic  State 187 

IX.    X-RAY  SPECTRA 192 

Introduction 192 

Critical  Potentials  for  X-Ray  Excitation        ....  193 

Absorption  Phenomena 196 

Emission  Lines  and  the  Combination  Principle     .      .  204 
Theoretical  Significance  of  the  System  of  Absorption 

Limits 209 

Conclusion 213 


CONTENTS  13 

CHAPTER  PAGE 

X.     PHOTO-ELECTRIC  EFFECT  IN  VAPORS 216 

XI.    DETERMINATIONS  OF  h  INVOLVING    LINE    SPECTRA  .     .  223 

Characteristic  X-Rays 223 

The  Rydberg  Number      ...            224 

lonization  and  Resonance  Potentials          225 

APPENDIX  I 227 

Computational  Data '.      .      .      .  227 

Nuclear  Defect,  Table  44  . 227 

Numerical  Magnitudes,  Table  45 228 

Velocities  of  Electrons,  Ions  and  Molecules   ....  229 
Periodic  Classification  of  Elements,  Table  46      .      .      .231 

APPENDIX  II.    BOHR'S  THEORY  OF  ATOMIC  STRUCTURE  .      .     .  232 

1st  Period 233 

2nd  Period 235 

3rd,  4th  and  5th  Periods 235 

6th  and  7th  Periods 235 

X-Ray  Spectra       . 237 

Superficial  Atomic  Properties 237 

Arc  and  Spark  Spectra 239 

Conclusion         240 

INDEX  OF  SUBJECTS 243 

INDEX  OF  AUTHORS  249 


Chapter  I 
The  Quantum  Theory  of  Spectroscopy 

The  quantum  theory  of  spectra  has  been  concerned  mainly  with  the 
Rutherford  type  of  atom.  This  consists  of  a  positive  nuclear  charge 
Ze,  where  Z  is  the  atomic  number,  surrounded  by  Z  electrons.  Practi- 
cally the  entire  mass  of  the  atom  is  concentrated  in  the  positive  core,  the 
size  of  which,  however,  is  much  smaller  than  that  of  an  electron.1  The 
electrons  are  usually  considered  as  revolving  about  the  nucleus  in 
coplanar  orbits.  Actually  there  is  evidence  that  the  orbits  are  not 
coplanar  and  models  have  been  proposed  in  which  the  electrons  do  not 
revolve  about  the  nucleus,  but  with  the  exception  of  helium  little  progress 
from  the  quantitative,  spectroscopic  and  mathematical  standpoints  has 
been  made  with  such  types  of  atom. 

Even  if  we  really  understood  the  precise  structure  of  a  heavy  atom, 
the  mathematical  analysis  of  the  orbits  would  be  hopeless  —  a  problem 
of  n  bodies  where  n  is  large.  Hence  the  exact  interpretation  of  spec- 
troscopic phenomena  is  a  problem  for  the  far-distant  future.  For  the 
present  bold  simplifying  assumptions  must  needs  be  made  for  the  purpose 
of  obtaining  results.  Postulates  are  proposed,  the  only  apparent 
justification  of  which  lies  in  the  applicability  of  the  conclusions  to  ex- 
perimental facts.  When  necessary,  the  fundamental  principles  of 
classical  dynamics  are  temporarily  abandoned  and  apparently  illogically 
accepted  for  later  steps  in  the  analysis  of  the  problem.  In  spite  of  such 
inconsistency  the  quantum  theory  of  spectra  is  the  only  satisfactory 
attempt  so  far  made  toward  interpreting  spectral  series  and,  already, 
by  predictions  from  theory,  has  led  to  experimental  verifications  of 
the  greatest  moment.  This  is  the  goal  of  any  theory;  not  necessarily 
to  explain  nature  but  to  aid  in  a  systematic  search  for  new  phenomena. 

l  The  mass  is  of  electromagnetic  nature.  As  appears  later,  the  ratio  of  the  mass  of  the 
hydrogen  nucleus  to  that  of  a  slow-moving  electron  is  about  1846.  Since  the  diameter  of  a 
spherical  charge  is  inversely  proportional  to  its  mass,  the  hydrogen  nucleus  should  have 
1/1846  the  diameter  of  an  electron.  The  best  guess  is  probably  10~16  cm  for  the  diameter 
of  this  nucleus,  but  any  estimate  involves  questionable  conjectures. 

15 


16  !      ORIGIN   OF  SPECTRA 

THE  SIMPLE  THEORY  OF  HYDROGEN  AND  IONIZED  HELIUM 
We  shall  first  consider  simple  atoms  containing  the  nucleus  and  a 
single  electron.  Such  an  atom  is  hydrogen,  ionized  helium,  or  doubly 
ionized  lithium.  Merely  by  way  of  introduction  we  shall  postulate  that 
the  electron  of  charge  —  e  for  hydrogen  revolves  in  a  circular  orbit 
about  the  nucleus  of  charge  -\-e.  Since  the  mass  of  the  electron  is  small 
compared  to  that  of  the  nucleus,  we  may  readily  derive  from  simple 
mechanics  the  total  energy  W  of  the  revolving  electron  (the  sum  of  the 
kinetic  and  potential  energies). 

W  =  _  *.         I  -  ™2  (1) 

2a>         a       e*  ' 

where  a  is  the  radius  of  the  circular  orbit,  m  the  mass  of  the  electron  and 
v  its  linear  velocity. 

So  far  as  ordinary  mechanics  is  concerned  a  may  have  any  value 
whatever,  depending  upon  "initial  conditions  ".  Bohr,2  however,  postu- 
lates that  only  certain  definite  sizes  of  orbits  are  permissible  stationary 
states,  so  determined  that 

2  TT  X  angular  momentum  =  nh,  (2) 

where  h  is  Planck's  universal  constant  of  action  and  n  may  assume 
integral  values  only.     Whence  : 

2  Trmav  =  nh. 

Substituting  this  in  the  relation  ma?vz  =  —  e*/2W  obtained  from  (1) 
we  find  for  Wn  the  total  energy  of  the  electron  in  the  nth  orbit  : 


In  order  for  this  to  be  a  stationary  state,  no  energy  can  be  radiated. 
On  the  basis  of  classical  dynamics,  however,  an  accelerated  electron 
emits  radiation  and  hence  the  electron  should  spiral  in  toward  the 
nucleus  instead  of  remaining  in  the  nth  orbit.  We  accordingly  postulate 
that  on  the  basis  of  the  quantum  theory  the  nth  orbit  is  a  stationary 
state  and  that  no  energy  is  radiated  so  long  as  the  electron  remains  in 
this  orbit.  If,  however,  it  should  jump  to  the  n'th  orbit  Bohr  further 
postulates  that  radiation  is  suddenly  emitted  of  such  frequency  v  that 

Wn  -  Wn.  =  hf.  (4) 

The  quantity  hv  is  known  as  a  quantum  of  energy  of  frequency  v  . 
Hence  in  any  interorbital  transition  a  single  quantum  of  radiation  is 

»  See  general  reference  1  at  end  of  chapter. 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         17 

emitted  (n  >  ri)  or  absorbed  (n  <  w'),  the  magnitude  of  which  (ex- 
pressed in  ergs  for  example)  is  equivalent  to  the  difference  in  total  ener- 
gies of  the  electron  in  the  two  orbits  concerned.  This  fact  is  simply  an 
application  of  the  principle  of  the  conservation  of  energy.  Substituting 
the  values  of  W  from  Equation  (3)  in  the  above,  we  obtain: 

2  Tr2m 


h* 

In  general  it  is  desirable  to  express  our  values  in  terms  of  wave 
number  v,  i.e.  the  reciprocal  of  the  wave-length  in  cm  in  vacuo.  Whence, 
since  v  =  v/c  where  c  is  the  velocity  of  light : 


/.r 

R  ' 


in  which 

_  2  •„  ,,n     _  N  ,-^ 

ch*  •*>'  W? 

The  subscript  <x>  is  sometimes  added  to  call  attention  to  the  fact 
that  we  have  assumed  the  mass  of  the  electron  as  negligible  compared  to 
that  of  the  core.  Formula  (6)  gives  to  a  high  degree  of  precision  all  the 
series  lines  of  the  hydrogen  atom.  With  n'  =  I,  n  =  2,  3,  etc.,  we  have 
the  Lyman  ultra-violet  series;  with  n'  —  2,  n=  3,  4,  etc.,  the  Balmer 
series;  and  with  n'  =  3,  n  —  4,  the  Paschen  series  of  infra-red  lines. 

If  we  consider  the  effect3  of  the  finite  mass  M  of  the  nucleus  we 
find  that  the  constant  N  in  (6)  must  be  replaced  by : 

NX  =      M     N    .  (8) 


This  is  appreciably  different  from  N&  for  hydrogen  as  well  as  for  other 
light  elements.  The  observed  value  of  NH  obtained  from  an  empirical 
consideration  of  the  series  lines  agrees  well  with  that  computed  by  (8) 
and  (7)  from  the  known  physical  constants  m,  e,  c  and  h.  For  ionized 
helium  we  may  derive  in  the  above  manner: 


The  factor  4  enters  because  of  the  nuclear  charge  Z  =  2  which  occurs  in 
the  derivation  as  Z2.  This  formula  again  represents  important  series 
lines,  formerly  attributed  to  hydrogen  but  now  known  to  be  due  to 
ionized  helium,  for  example  the  series  n'  =  3,  n  =  4,  5,  etc.,  also  n'  =4, 
n  =  5,  6,  etc. 

3  Both  nucleus  and  electron  revolve  around  the  common  center  of  mass.    In  this  and 
following  developments  we  are  concerned  with  the  energy,  momentum,  etc.,  of  the  entire 

system,  not  of  the  electron  alone.    The  substitution  of     "*jf"     for  ™  in  the  above  equations 
.    takes  account  of  this. 


18  ORIGIN  OF  SPECTRA 

RATIO  OF  MASS  OF  HYDROGEN  NUCLEUS  AND  HYDROGEN  ATOM  TO 
MASS  OF  ELECTRON,  AND  VALUE  OF  e/m 

From  empirically  determined  values  of  AH  and  ArHe  it  is  possible 
to  obtain  the  ratio  of  the  mass  of  the  hydrogen  atom  to  that  of  an 
_  electron.     Paschen  finds  empirically: 

NH   =  109677.691     ] 
ArHe  =  109722.144  (10) 

and  through  Equation  (8)       N*    =  109737.11 

mass  of  helium  atom     _  M'He  _    4.00 
mass  of  hydrogen  atom  ~~  M'H      1.0077 

from  atomic  weight  determinations. 

mass  of  helium  nucleus     _  MHe  _ 
mass  of  hydrogen  nucleus       MH 

From  Equation  (8)  it  follows  that: 

MH  _      mass  of  hydrogen  nucleus  x 

m    ~  mass  of  slow-moving  electron       AHC  —  AH 

But  ^|~5?  =  ^e  "t  2^m  =  3.969. 

'  Hence  x  =  1.969  ^-  +  3.969. 

Assume  1900  >  —  >  1800.     Then  x  =  3.970. 
m 

Accordingly,  from  Equations  (10)  and  (11), 

MH  mass  of  hydrogen  nucleus      _  .„.„  _ 

m         mass  of  slow-moving  electron 

A   H  -^TH  _        mass  of  hydrogen  atom        _  MH  +  m  _  |        „ 

m        mass  of  slow-moving  electron  m 

This  value  agrees  well  with  that  obtained  by  other  methods. 

Mi  /  / 

H        £/  in        e/m 
Furthermore  -  =     ,..,    =  —7- , 

m        e/M'H        f 

where  /  is  the  value  of  the  Faraday.     VinaPs 4  most  recent  work  shows 

*  Vinal,  Bur.  Standards  Sci.  Papers,  218  and  271. 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         19 

that  this  is  not  known  with  quite  the  precision  ordinarily  assumed,  his 
extensive  experiments  giving  /  =  96500  ±  10  coulombs.    Accordingly 


_e  mjMj*  =  (96500)  (1846.5)  =  1.7819  - 108  coulombs/g  1 


(12) 


=  1.7819- 107e.m.u./g 
=  5.343    •  1017  e.s.u./g.      J 

These  values  should  be  good  to  1  part  in  2000  so  that  the  method  affords 
one  of  the  most  precise  means5  for  determining  e/m. 

ELLIPTICAL  ORBITS 

The  possibility  of  elliptical  orbits  for  the  revolving  electron  greatly 
complicates  the  problem  by  the  introduction  of  a  second  degree  of 
freedom,  viz.  variation  in  the  length  of  the  radius  vector,  but  leads  to 
results  of  the  most  fundamental  nature. 

In  general,  let  us  consider  a  system  having  k  degrees  of  freedom. 
For  the  description  of  its  configurations  we  require  k  independent  co- 
ordinates, q\,  q*  •'  •  •  q*.  These  may  be,  for  example,  the  Cartesian  or 
the  polar  coordinates  of  the  various  particles  of  the  system.  Cor- 
responding to  each  q  there  will  be  a  quantity  p  which  plays  the  same 
mathematical  role  in  the  expression  for  the  kinetic  energy  of  the  system 

as  the  components  of  momentum,  m  -^- ,  m  -j- ,  m-^  play  in  the  formula 

dt        o/t       dt 

for  the  kinetic  energy  of  a  single  particle.     Thus  for  a  particle,  in  Carte- 
sian coordinates,  the  kinetic  energy, 


where  px,  py,  and  pz  are  the  components  of  momentum.     It  will  be 
noted  that  if  we  write  -^  =  vx,  etc.,  then 

dT      dT      m 
M  =  to,  =  2 

and  similarly  for  pv  and  pz. 

5  This  statement  is  based  on  Paschen's  estimate  of  the  precision  with  which  NH  and 
A7He  may  be  empirically  determined.  -  Birge,  Phys.  R.  17,  pp.  589-607  (1921),  in  a  very 
thorough  consideration  of  the  measurements  on  the  hydrogen  lines,  has  concluded  that 
iVH  =  109677.7  =t  0.2.  An  uncertainty  of  ±  0.2  in  NH  gives  rise  to  a  possible  error  of 
=*=  0.5%  in  JVHe  —  NH  of  Equation  (11),  which  is  carried  over  directly  in  the  final  compu- 
tation of  dm.  A  similar  error  in  -ZVHe  would  still  further  increase  the  uncertainty  in  the  deter- 
mination of  elm. 


20  ORIGIN  OF  SPECTRA 

Likewise  for  any  dynamical  system  we  define  the  generalized  moment 
Pt  corresponding  to  the  coordinate  qt  to  be 


Let  us  choose  such  generalized  coordinates  that  the  kinetic  energy 
contains  only  the  squares  of  the  generalized  moments  pt,  so  that  no  terms 
such  as  pip2  occur.  In  general  the  square  of  each  moment  will  be  pre- 
fixed by  a  coefficient  which  may  be  a  function  of  one  or  more  of  the 
coordinates  q.  For  example,  the  expression  for  the  kinetic  energy  of  a 
particle  of  mass  m  in  polar  coordinates  is 


-£  =  pr  =  linear  momentum  in  the   direction  of  the  radius  vector; 

-f  —  p.  =  angular  momentum  about  the  origin. 
at 


Therefore  T  =  ^(^  +  -2, 

Let  the  coordinates  also  be  so  chosen  that  the  potential  energy  of 
the  system  consists  of  a  sum  of  functions  each  of  which  depends  upon 
one  coordinate  only.  Thus  the  potential  energy  will  have  the  form 


For  all  the  systems  with  which  we  shall  deal,  such  a  choice  of  co- 
ordinates is  possible. 

The  conditions  by  which  we  select  discrete  or  quantized  states  of 
steady  non-radiating  motion  for  the  dynamical  system  of  the  atom  may 
be  stated  in  terms  of  the  above  generalized  coordinates  as  follows : 

f  ptdqt  =  nji 

dT 

where  ^"^ 

and  where  the  integral  is  taken  over  a  complete  period  of  the  coordinate 
in  question.  (We  shall  be  concerned  only  with  systems  where  each 
coordinate  is  periodic.)  The  k  equations  furnished  by  the  above  re- 
quirements are  the  quantizing  conditions  laid  down  independently  by 
W.  Wilson6  and  by  Sommerfeld.7 

«  W.  Wilson,  Phil.  Mag.  29,  p.  795  (1915). 

»  Sommerfeld,  "Atombau,"  any  edition,  preferably  3d. 


THE  QUANTUM  THEORY  OF  SPECTROSCOPY         21 

As  an  example  of  the  application  of  Equations  (13)  let  us  consider 
first  the  simple  case,  described  earlier,  of  circular  orbits.  Here  we  have 
but  one  degree  of  freedom,  the  azimuth  <f>,  since  the  radius  vector  is 
fixed  in  magnitude.  The  limits  of  integration  are  <£  =  0  and  0  =  2  T, 
corresponding  to  one  complete  revolution  of  the  electron.  Thus: 


T  =  ^ 


dT      dT 

a*-  a? 


Hence  f  pdq  =  f     mr^dQ  =  2  irmr2^  =  nah 

* 


since  <j>  is  constant.  But  wr20  is  the  angular  momentum  of  the  electron. 
We  have  accordingly  derived  Equation  (2)  by  the  use  of  the  more  gen- 
eral relation  (13). 

The  integer  na  in  this  case  is  known  as  the  azimuthal  quantum 
number  since  the  integral  to  which  it  applies  contains  the  azimuth  as 
the  independent  variable. 

In  the  case  of  elliptical  motion  the  quantizing  process  must  be 
applied  in  respect  to  both  azimuth  and  radius  as  follows  : 

2  TT    •J'TT 

azimuth  :   nji  =  f  pdq  =  f     —  -  d<j>  =  2  TT  X  angular  momentum    (14) 
J  J  o     d<p 

2  TT        ^  ^T* 

radius:       nrh  =  f  pdq  =  f       -rr  dr.  (15) 

The  integer  nr  is  known  as  the  radial  quantum  number  since  the  in- 
dependent variable  in  Equation  (15)  is  the  radius  r.  If  we  substitute 
in  this  the  value  of  the  kinetic  energy  we  obtain  from  (14)  and  (15) 


in  which  e  is  the  eccentricity  of  the  elliptical  orbit.  Thus  not  only 
must  the  angular  momentum  of  the  electron  have  certain  discrete 
values  but  at  the  same  tune  the  shapes  of  the  elliptical  orbits  are  re- 
stricted in  a  very  definite  manner. 

If  we  now  evaluate  the  total  energy  Wn<Jnr  of  the  electron  in  any 
particular  ,orbit  determined  by  the  azimuthal  quantum  number  na  and 
the  radial  quantum  number  nr,  we  find 

Nhc 


22 


ORIGIN  OF  SPECTRA 


It  will  be  noted  that  several  different  orbits  exist,  depending  upon  how 
the  total  value  of  na  +  nr  is  obtained,  for  which  the  energy  has  the  same 
value.  For  example  the  orbit  na  =  1,  nr  =  2  has  the  same  energy  as  the 
orbit  na  =  2,  nr  =  1  since  na  +  nr  =  3  in  each  case. 


Scale 


FIG.  1.  A  few  of  the  inner  orbits  wh:ch  may  be  occupied  by  the  electron  of  the 
hydrogen  atom.  Actually  these  orbits  are  perturbed  so  that  they  are  not 
exactly  closed  or  cyclic.  There  is  present  a  slow  progressive  mot:on  of  peri- 
hel  on.  The  illustrat'on  represents  very  closely  an  ''instantaneous  photograph" 
of  the  possible  states,  while  a  "tims  expos  are"  would  give  a  solid  field  of  ink  on 
account  of  the  progressive  motion. 

Proceeding  now  in  the  same  manner  as  that  in  which  Equation  (6) 
was  derived  and  putting  the  difference  in  the  total  energies  of  two  orbits 
WnaTlr  and  Wn,an,r  equal  to  h  times  the  frequency  of  the  emitted  radi- 
ation, or  he  times  the  wave  number  v,  we  obtain  the  following  spectral 
series  formula : 


V  = 


(18) 


This  again  represents  the  series  lines  of  hydrogen.  The  Balmer  series  is 
obtained  when  n'a  -f  rir  =  2  and  na  +  nr  =  3,  4,  5,  etc.  The  physical 
significance  of  this  more  complicated  formula  will  appear  later. 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         23 

It  may  be  readily  shown  that  all  elliptical  orbits,  for  which  the  total 
energy,  W,  of  the  atom  is  the  same — cf.  Equation  (17) — have  equal  semi- 
major  axes,  a,  and  that  the  semi-minor  axes,  6,  have  the  magnitudes: 


nf, 


nr 


a. 


(19) 


All  orbits  for  which  na  —  0  are  straight  lines  through  the  nucleus  and 
are  hence  excluded  as  physically  impossible.  We  shall  consider  the 
form  of  the  various  inner  orbits  for  the  hydrogen  atom,  subject  to  the 
condition  na  ^  0.  The  inmost  orbit  is  obtained  when  na  +  nr  =  1,  that 
is,  when  na  =  1,  nr  =  0,  The  next  group  of  orbits  is  found  by  making 
na  +  nr  =  2.  Proceeding  in  this  manner  we  may  by  the  help  of  Equa- 
tion (19)  compute  the  constants  of  the  orbits,  as  given  in  Table  I, 
and  further  illustrated  by  Figure  1. 


TABLE   I 
ORBITS  OF  HYDROGEN  TO  na  +  nr  =  4 


na  +  nr 

na 

nr 

a 

6 

Form  of  Orbit 

1 

1 

0 

di 

ai 

circle 

2 

2 

0 

4«i 

4ai 

circle 

2 

1 

1 

4oi 

20! 

ellipse 

3 

3 

0 

9ai 

9«i 

circle 

3 

2 

1 

9ai 

6ai 

ellipse 

3 

1 

2 

9ai 

3ai 

ellipse 

4 

4 

0 

I6ai 

16«i 

circle 

4 

3 

1 

16ai 

12ai 

ellipse 

4 

2 

2 

16ai 

8ai 

ellipse 

4 

1 

3 

16ai 

•4ai 

ellipse 

The  line  Ha  is  produced  by  an  electron  jumping  from  an  orbit  na  +  nr  =  3 
to  an  orbit  na  -f  nr  =  2.  Since  there  are  three. orbits  of  equal  energy 
value  for  which  na  +  nr  =  3  and  two  orbits  for  which  na-\-nr  =  2,  the 
line  Ha  may  be  produced  in  six  different  ways.  Similarly  H0  and  H7 
may  be  produced  in  eight  and  ten  different  ways  respectively.  These 


24  ORIGIN  OF  SPECTRA 

conclusions,  however,  must  be  considerably  modified,  as  will  appear 
directly.8 

RELATIVITY  OF  MASS 

The  first  modification,  due  to  Sommerfeld  9,  arises  in  the  fact  that  the 
mass  of  the  electron  in  its  elliptical  orbit  is  not  a  constant  but  depends 
upon  its  velocity,  v,  thus  :m  =  m0  v  1  —  /32,  where  0  =  v/c  and  m0  is  the 
mass  of  a  stationary  or  slow-moving  electron.  From  a  mathematical 
standpoint  the  character  of  the  orbit  is  considerably  changed  thereby, 
but  if  the  velocity  of  the  electron  is  moderate  compared  to  that  of  light, 
we  may  consider  the  path  as  an  ellipse  with  slowly  moving  perihelion. 
Corresponding  to  Equation  (17)  we  now  obtain  Equation  (20)  for  the 
energy  of  the  electron  in  the  nanr  orbit. 


where          a  =  -T—-  •  (21) 

In  this  relation  o?  is  a  relatively  small  quantity  being  equal  to  5.31  •  10~5; 
hence  it  is  sufficient  for  the  present  to  neglect  terms  of  higher  order 


s  It  is  of  interest  to  note  that  there  exists  a  perfectly  general  relation  between  the  fre- 
quency of  revolution  of  the  electron  about  the  nucleus  and  the  wave  number  or  the  frequency 
of  the  radiation  emitted  when  the  electron  falls  from  one  orbit  to  another. 

It  may  be  readily  shown  that  the  frequency  of  revolution,  L.  of  the  electron  moving  in 
an  elliptical  orbit  about  the  positive  cha'rge  E  is  given  by  the  relation 


where     a= 


On  replacing  a  in  the  first  equation  by  its  equivalent,  we  obtain 

(by  Equation  7) 
or,  for  hydrogen,  /  =       z_f  c  for  the  initial  orbit 

(Tla  -f-  nr)  * 

and  /'  =  ,.,/2f7f/xt  for  the  final  orbit. 

Replacing  the  terms  (na  +  nr)2  and  (n'a  +  n'r)»  of  Equation  (18)  by  the  values  from  the 
above  relations  we  find  directly 

If  this  is  expressed  in  terms  of  the  total  quantum  number  n  »  no  +  nr  and  frequency  v 
(  =  cv)  instead  of  v,  we  obtain 

Hence  the  frequency  of  the  emitted  radiation  is  one-half  the  difference  of  the  products  of 
the  total  quantum  number  and  the  frequency  of  revolution  of  the  electron  in  each  of  the 
orbits  concerned  in  the  transfer.  This  is  a  general  law  immediately  applicable  to  any  spec- 
truin  of  the  hydrogen  type,  such  as  that  of  ionized  helium,  doubly  ionized  lithium,  etc.  If 
n  —  n'  =  1  where  both  n  and  n'  are  large  v  ~  f,  that  is,  the  frequency  of  the  emitted  light  is 
approximately  equal  to  the  frequency  of  revolution  of  the  electron  in  its  orbit.  This  approxi- 
mation of  the  quantum  theory  to  the  classical  dynamics  for  small  frequencies  or  long  wave- 
lengths has  an  analogy  in  the  law  of  the  spectral  distribution  for  black-body  emission,  where 
the  Planck  relation  approximates  the  classical  Rayleigh  equation  for  long  wave-lengths. 
•  See  general  reference  3  at  end  of  chapter. 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         25 


than  a2.  The  first  term  of  this  general  equation  is  identical  with  Equa- 
tion (17)  (for  hydrogen,  Z  =  1).  The  second  and  succeeding  terms  are 
the  corrections  introduced  by  the  relativity  considerations.  We  note  that 
whereas  in  Equation  (17)  na  and  nr  occurred  together  as  a  sum,  in  the 
correction  term  of  Equation  (20).  they  also  occur  as  a  quotient.  The 
energies  of  the  various  "  elliptical"  orbits  in  Figure  1,  for  the  same  total 
quantum  number  accordingly  depend  upon  how  this  number  is  obtained. 
For  example  the  energy  is  slightly  different  for  the  orbits  characterized 
by  na  +  nr  =  1  +  2  =  3;  na  +  nr  =  2  +  1  =  3  and  na  +  nr  =  3  + 
0  =  3.  Thus  the  six  possible  transfers  from  na  +  nr  =  3  to  na  +  nr  =  2 
will  produce  six  slightly  different  frequencies.  These  frequencies  or 
wave  numbers  may  be  computed  from  Equation  (22)  which  is  analogous 
to  Equation  (18)  derived  without  relativity  considerations. 


Hence  the  line  H«  which  represents  an  interorbital  transfer  from 
total  quantum  numbers  3  to  2,  when  resolved  by  a  high  power  spectro- 
scope such  as  an  echelon  grating,  should  show  fine  structure  and  should 
appear  as  a  group  of  fine  lines.  The  six  mathematically  possible  com- 
ponents for  Ha,  computed  by  Equation  (22)  ,  where  for  N  is  substituted 
N-B.  thus  taking  into  account  the  finite  mass  of  the  nucleus,  are  given  in 
Table  II. 

TABLE   II 
FINE  STRUCTURE  OF  Ha 


V 

X 
Vacuum 

nanr  -»  n'arir 

Ana 

Remarks 
See  page  26 

r15233.451 

6564.501 

30->11 

-  2 

excluded 

3.415 

.516 

21-+11 

-  1 

rj            3.307 

.563 

12-»11 

0 

excluded 

3.086 

.658 

30  -^  20 

-  1 

3.050 

.674 

21  -+20 

0 

excluded 

2.941 

.720 

12->20 

+  1 

In  the  same  manner  the  fine  structure  of  other  Balmer  lines  and  lines 
of  the  Lyman  and  Paschen  series  may  be  computed.    With  Z  =  2  in 


26  ORIGIN  OF  SPECTRA 

Equation  (22)  we  may  similarly  predict  the  fine  structure  of  the  series 
lines  of  ionized  helium. 

THE  PRINCIPLE  OF  SELECTION 

The  second  modification  of  the  simple  theory  consists  in  the  applica- 
tion of  the  principle  of  selection.  So  far  in  the  analysis  we  have  utilized 
the  principle  of  the  conservation  of  energy  as  applying  to  the  coupled 
action  between  the  ether  and  matter.  The  energy  lost  by  the  atom 
when  the  electron  is  transferred  from  an  orbit  of  higher  energy  level  to 
one  of  lesser  energy  is  conserved  by  the  ether  in  the  form  of  radiation  of 
frequency  v  or  wave,  number  v  given  by  Equation  (22) .  Keeping  the 
original  Bohr  postulates  which  included  the  principle  of  conservation  of 
energy  we  shall  now  additionally  restrict  the  problem  by  the  condition 
that  we  have  conservation  of  moment  of  momentum.10  That  is,  the 
moment  of  momentum  lost  by  the  mechanical  system  forming  the 
atom,  in  any  interorbital  transition,  is  conserved  by  the  ether  as  moment 
of  momentum  of  radiation.  By  a  simple  mathematical  analysis  Rubin- 
owicz11  showed  that  these  assumptions  lead  to  the  conclusions  that  in 
any  interorbital  transition  of  an  electron,  resulting  in  radiation,  and 
not  complicated  by  the  presence  of  an  electrostatic  or  magnetic  field, 
the  azimuthal  quantum  number  na  may  change  by  —  1,  0  or  -|-  1  and 
by  no  other  amount.  Bohr12  has  derived  a  more  restricted  principle  of 
selection  which  excludes  the  zero  change  of  momentum.  For  the  present 
we  shall  confine  our  discussion  to  the  Bohr  restricted  principle  which 
may  be  stated  as  follows: 

A  na  =  ria  -  na  =  +  1  or  -  1.  (23) 

Applying  this  principle  to  the  analysis  of  the  fine  structure  of  Ha, 
of  the  six  mathematically  possible  transitions  three  are  excluded  as 
shown  in  the  last  two  columns  of  Table  II,  because  for  these  the  change 
in  azimuthal  quantum  number  is  not  =b  1.  Hence  we  arrive  at  the 
final  conclusion  that  the  line  Ha  is  made  up  of  three  components.  On 
account  of  the  difference  in  energy  of  the  two  final  orbits,  na  -f  nr  =  1  -f- 1 
and  na  +  nr  =  2  +  0,  these  three  lines  may  be  considered  as  a  doublet 
one  component  of  which  has  a  satellite.  Similarly  with  H^  for  which, 
of  the  4X2  =  8  mathematically  possible  transitions,  all  but  three  are 
excluded  by  the  selection  principle.  The  interorbital  transitions  result- 
ing in  H«  and  H0  are  shown  by  dotted  lines  in  Figure  1 . 

10  For  a  concise  statement  of  the  conceptions  here  involved,  see  Sommerfeld,  "Atombau," 
3d  Ed.,  pp.  310-39. 

11  Rubinowicz,  Physik.  Z.  19,  pp.  441,  465  (1918). 

12  See  general  reference  2.    Also  Dushman,  J.  Opt.  Soc.  Am.  &  R.  S.  I.,  6,  p.  235  (1922). 


THE   QUANTUM   THEORY  OF  SPECTROSCOPY         27 


EXPERIMENTAL  VERIFICATION  BY  FINE  STRUCTURE  ANALYSIS 

The  experimental  verification  of  the  above  deductions  in  the  case 
of  the  hydrogen  atom  is  probably  as  satisfactory  as  could  be  expected 
at  the  present  time.  Referring  to  Table  II  it  is  seen  that  the  entire  fine 
structure  of  Ha  should  cover  a  spectral  range  of  only  0.2  A.  Now  the 
width13  of  a  spectral  line,  assuming  it  may  be  accounted  for  by  the 
Doppler-Fizeau  effect,  may  be  shown14  to  be 

A  =  0.86  ao~6  \VTYM; 

where  T  is  the  absolute  temperature  and  M  the  molecular  weight  of  the 
radiating  gas. 

Since  M  =  1  for  the  hydrogen  atom  it  is  readily  apparent  that  the 
precision  of  measurement  of  fine  structure  will  be  seriously  affected 
by  the  Doppler  effect.  Even  with  the  discharge  tube  immersed  in 
liquid  air  the  theoretical  width  of  each  component  of  Ha  is  0.051  A. 
However,  the  component  of  longest  wave-length  should  be  weak,  and  it 
may  be  shown  that  the  separation  of  this  component  and  the  central 
component  should  be  only  about  4/10  the  separation  of  the  central 
component  and  the  one  of  shortest  wave-length.  This  results  in  the 
obervation  of  the  triplet  as  a  doublet  with  fairly  wide  components  arising 
from  the  Doppler  effect.  The  observed  separation  of  this  doublet 
is  obviously  not  the  theoretical  doublet  separation  shown  by  the  braces 
in  the  first  column  of  Table  II,  which  has  the  computed  magnitude 
A*>H  =  0.365  cm"1.  It  is  possible  to  compute  from  the  theoretical  distri- 
bution of  the  lines  what  magnitude  of  the  doublet  separation  should  be 
observed.  Or  conversely,  the  observed  separations  when  corrected 
should  afford  a  check  upon  the  theoretical  deductions.  We  have,  how- 
ever, in  addition  to  the  distribution  of  intensity  produced  by  the  Doppler 
effect,  in  any  laboratory  experiment,  broadenings  of  each  component 
arising  in  the  Stark  effect,  imperfect  focus  upon  the  plate,  spreading 
of  the  image  on  the  emulsion,  and  mechanical  difficulties.  These 
effects  combine  in  producing  an  apparent  narrowing  of  the  observed 
doublet.  The  following  table  summarizes  the  data  on  H«  by  several 
observers  where  we  are  not  certain  of  the  methods  employed  in  deter- 
mining these  various  correction  factors.  In  fact,  some  of  these  cor- 
rections have  not  been  applied  to  the  first  three  values  given.  * 

13  Measured  at  the  point  where  the  intensity  has  decreased  to  1  !e  of  its  maximum  value. 

14  The  method  of  derivation  of  this  and  similar  formulae  is  summarized  by  Nagaoka, 
Proc.  Math.  Phys.  Soc.  Tokyo,  8,  pp.  237-43  (1915). 


28 


ORIGIN  OF  SPECTRA 


AVB. 

Observer 

Reference 

.34  cm-1 
.29 
.36 
.35 

Merton 
Gehrcke  and  Lau 
McLennan  and  Lowe 
Oldenberg 

Proc.  Roy.  Soc.  97,  p.  307  (1920) 
Physik.  Z.  21,  p.  634  (1920) 
Proc.  Roy.  Soc.  100,  p.  217  (1921) 
Ann.  Physik,  67,  p.  453  (1922) 

It  is  seen  that  the  agreement  between  the  observed  and  computed 
values  is  fairly  satisfactory.  However,  when  the  measurements  are 
extended  to  other  lines  in  the  Balmer  series  there  appears  to  be  a  slight 
systematic  decrease  in  the  doublet  separation,  measured  in  cm"1,  as  one 
proceeds  to  the  higher  terms  of  the  series.  It  is  doubtful  whether  the 
above-mentioned  disturbing  effects  are  adequate  to  account  completely 
for  existing  observations  on  H0,  H7,  and  Hj.  Ruark  has  suggested  to 
the  authors  that  there  still  remain  to  be  considered  disturbances  arising 
in  (1)  finite  size  of  nucleus15  and  (2)  possible  magnetic  moment  of 
nucleus.  Any  correction  arising  from  a  consideration  of  retarded  po- 
tentials has  been  shown  by  Darwin16  to  be  less  than  0.001  A  and  to 
affect  all  components  of  a  given  line  in  the  same  mariner. 

The  real  experimental  verification  of  the  theory  lies  in  Paschen' s 
analysis  of  certain  lines  of  ionized  helium.17  Since  for  helium  M  =  4 
the  Doppler  effect  is  considerably  decreased,  and  since  Z  =  2  we  have 
a  more  open  scale  of  v,  as  is  apparent  from  Equation  (22) .  The  helium 
line  X  4686  is  produced  by  a  transfer  of  the  remaining  electron  in  the 
ionized  atom  from  orbits  of  total  quantum  number  4  to  orbits  of  total 
quantum  number  3.  Twelve  lines  are  thus  mathematically  possible, 
but  the  application  of  the  Bohr  principle  of  selection  reduces  this  number 
to  five.  Figure  2,  adapted  from  SommerfekTs  "Atombau,"  2d  ed.,  p. 
350,  shows,  below,  the  wave-lengths  observed  by  Paschen,  the  heights 
of  the  shaded  portions  representing  intensity.  Above  the  observed 
wave-lengths  are  those  computed  by  means  of  Equation  (22),  using  the 
selection  principle.  At  the  top,  shown  by  dotted  lines,  are  the  mathe- 
matically possible  lines  computed  directly  from  Equation  (22).  The 
entire  wave-length  scale  covers  an  interval  of  only  0.8  A.  or  about  £ 
of  the  distance  between  the  two  D-lines  of  sodium,  and  yet  the  theoreti- 
cally predicted  fine  structure  is  well  confirmed  by  the  experimental 

14  Silberstein,  Phil.  Mag.  39,  p.  46  (1920),  has  given  the  method  of  computing  correc- 
tions for  an  aspherical  nucleus, 
is  Phil.  Mag.  39,  p.  537  (1920). 
i?  Paschen,  Ann.  Physik,  50,  pp.  901-40  (1916). 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         29 

data.  The  two  lines  marked  d,  while  mathematically  possible,  involve 
a  change  in  the  azimuthal  quantum  number  of  two  units  and  hence  by 
the  principle  of  selection  should  not  exist.  However,  this  principle  was 
established  conditionally  upon  the  absence  of  an  electrostatic  or  electro- 
magnetic field.  On  the  other  hand  such  a  field  is  present  in  a  high 
voltage  discharge  tube.  A  thorough  consideration  of  the  phenomena 
in  the  presence  of  disturbing  fields  requires  the  application  of  the  quan- 
tum theory  to  the  Stark  and  Zeeman  effects,18  quite  beyond  the  scope 
of  the  present  work.  Suffice  to  say  that  as  a  result  of  such  analysis 
it  may  be  shown  that  the  lines  marked  d  should  appear  in  a  weak  elec- 
trostatic field,  and  still  other  lines  should  be  excited  with  higher  poten- 
tials, in  agreement  with  further  observations  of  Paschen.19 


X   4686.0        5.8  5.6  5.4 

FIG.  2.    Fine  structure  of  the  helium  line  X  4686. 


In  the  case  of  Ha  we  have  seen  that  the  fine  structure  consists  of  a 
fundamental  doublet  with  a  satellite.  The  doublet  separation  AJ/H 
is  due  to  the  difference  in  energy  of  the  two  final  orbits  1  +  1  =  2  and 
2  +  0  =  2.  This  value  of  A*/H  is  readily  obtained  from  Equation  (22) 
by  putting  AJ>  =  PI  —  v%,  where  *>i  refers  to  ria  =  1,  n'r  =  I  and  any 
value  of  na  and  nr  and  where  v%  refers  to  n'a  =  2,  rir  =  0  with  the  same 
values  of  na  and  nr.  Hence  since  Z  =  1  for  hydrogen,  we  obtain 


(24) 


r  =0.365  cm'1 
lo 


18  Kramers,  Copenhagen  Acad.,  1919.    See  also  general  references  2,  3,  4,  6,  7,  at  end  of 
chapter. 

19  Paschen,  loc.  clt. 


30  ORIGIN  OF  SPECTRA 

Now  Equation  (22)  may  be  rewritten  with  Na2  replaced  by  16  AvH  and 
the  new  formula  used  for  estimating  the  separation  of  the  components 
of  the  helium  lines  in  terms  of  AJ>H-  Or  conversely,  these  separations 
may  be  determined  experimentally  for  helium  and  used  to  compute  the 
value  of  AJ>H  for  hydrogen.  In  this  latter  manner  Paschen  found  experi- 
mentally 

AI/H  =  0.3645  db  0.0045  cm"1, 

in  agreement  with  the  theoretical  value  of  AvH  given  by  Equation  (24). 

ATOMS  WITH  MANY  ELECTRONS 

Evidence  from  various  sources,  both  physical  and  chemical,  enables 
us  to  derive  some  information  in  regard  to  the  distribution  of  electrons 
about  the  nucleus.  The  periodic  table  of  chemical  elements  furnishes 
an  important  clue  as  to  the  electron  arrangement.  The  present  view- 
point is  that  the  intervals  between  rare  gases,  and  not  the  rows  of  the 
table,  give  the  true  periods  of  the  atomic  systems. 

The  chemical  inactivity  of  the  rare  gases  suggests  that  these  elements 
represent  completed  structures.  With  the  intermediate  elements  only 
superficial  changes  in  the  electron  configuration  occur.  At  each  new 
period  a  "  shell"  is  added  to  the  original  structure.  An  atom  is  char- 
acterized by  as  many  groups  or  "  shells"  of  electrons  as  the  numerical 
value  of  the  period  which  it  occupies,  viz.,  He  one,  A  three,  etc.  The 
number  of  electrons  in  each  group  when  completed  has  been  considered 
equal  to  the  number  of  elements  in  the  corresponding  period.  That  is, 
in  successive  groups  from  the  center  out,  the  number  of  electrons,  on 
this  hypothesis,  follows  the  distribution  law  2,  8,  8,  18,  18,  32. 

The  new  Bohr20  theory  of  atomic  structure  retains  the  above  concep- 
tion of  groups  of  electrons  corresponding  to  periods  in  the  chemical  prop- 
erties but  postulates  the  occurrence  of  changes  in  inner  groups  as  well  as 
in  the  outer  shell.  The  resulting  distribution  for  several  families  is  given 
in  Table  III,  in  which  K,  L,  M,  etc.,  follow  the  usual  x-ray  notation  for 
successive  layers. 

As  to  the  orientation  of  these  electrons,  many  different  theories 
have  been  proposed.  The  Lewis-Langmuir21  hypothesis  postulates 
for  each  group  a  cubical  distribution  of  electrons  in  which  motions  are 
limited  to  relatively  small  vibrations  about  positions  of  equilibrium. 
Such  a  model  is  not  easily  reconciled  with  the  viewpoint  of  the  spec- 
troscopist. 

2°  Bohr,  Z.  Physik,  9,  pp.  1-67  (1922). 

21  Langmuir,  J.  Am.  Chem.  Soc.,  38,  p.  762  (1916);   41,  p.  868  (1919). 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY 

TABLE   III 
GROUPING  OF  ELECTRONS  IN  ATOMS 


31 


Element 

Z 

K 

L 

M 

N 

0 

P 

Q 

He.. 

Ne....  
A  
Kr  ......... 
Xe  

Nt   .   ... 

2 
10 
18 
36 
54 
86 

2 
2 
2 
2 
2 
2 

8 
8 
8 
8 
8 

8 
18 
18 
18 

8 
18 
32 

8 
18 

8 

|  Li  . 

3 

2 

1 

Na  

11 

2 

8 

1 

K  .. 

19 

2 

8 

8 

1 

Cu 

29 

2 

.  8 

18 

1 

Rb  

37 

2 

8 

18 

8 

1 

Ag  

Cs 

47 
55 

2 
2 

8 
8 

18 
18 

18 
18 

1' 

8 

1 

Au  .  .   . 

79 

2 

8 

18 

32 

18 

1 

Be 

4 

2 

2 

Mg. 

12 

2 

8 

2 

Ca.  . 

20 

2 

8 

8 

2 

Zn  

30 

2 

8 

18 

2 

Sr  

38 

2 

8 

18 

8 

2 

Cd  . 

48 

2 

8 

18 

18 

2 

Ba  

56 

2 

8 

18 

18 

8 

2 

Hg.. 

80 

2 

8 

18 

32 

18 

2 

& 
-  Ra 

88 

2 

8 

18 

32 

18 

8 

2 

The  configuration  originally  proposed  by  Bohr22  and  generally  adopted 
in  the  past  for  the  extension  of  the  Bohr  theory  to  atoms  with  many 
electrons,  consisted  of  coplanar,  concentric  rings  of  electrons  revolving 
about  the  nucleus.  The  possibility  of  elliptical  orbits  complicates  the 
problem,  for  while  several  electrons  may  be  stable  in  the  same  circular 
orbit  only  one  electron  may  occupy  an  elliptical  orbit.  However,  it  is 
readily  possible  to  so  orient  a  group  of  similar,  coplanar,  confocal  ellipses, 
each  containing  one  electron,  that  at  every  instant  all  the  electrons  of. 
any  one  group  lie  on  a  circle  concentric  with  the  nucleus. 

The  recently  proposed  theory  of  Bohr  (see  Appendix  II)  on  which 
the  distribution  of  electrons  in  Table  III  is  based,  denies  the  possibility 
of  the  formation  of  a  ring  model,  in  spite  of  its  mechanical  stability, 

22  See  general  reference  1  at  end  of  chapter. 


32  ORIGIN  OF  SPECTRA 

and  assumes  that  each  electron  moves  in  an  individual  orbit  and  in 
general  in  an  individual  plane.  The  resulting  space  configuration 
through  which  the  chemical  properties  of  the  elements  may  be  inter- 
preted leads  to  insurmountable  difficulties  in  the  mathematical  analysis 
of  the  motion  of  the  electrons  in  heavy  atoms,  except  for  qualitative 
deductions. 

Accordingly,  while  recognizing  that  the  electrons  are  actually  re- 
volving in  elliptical  orbits  in  different  planes,  orbits  such  that  those  of 
greater  quantum  number  and  eccentricity  may  penetrate  nearer  to  the 
nucleus  than  those  of  lesser  quantum  number  but  more  nearly  circular, 
we  shall  for  the  simplification  of  the  mathematical  treatment  adopt 
the  Sommerfeld23  conceptions. 

That  the  postulating  of  a  ring  configuration  for  the  inner  electrons 
frequently  is  an  approximation  to  fact  which  is  justified  as  far  as  the 
motion  of  an  outer  electron  is  concerned  will  be  evidenced  by  the  striking 
experimental  verification  of  the  conclusions  drawn  in  the  following 
sections. 

DERIVATION  OF  THE  RITZ  EQUATION 

The  Ritz  equation  represents  the  variable  term  in  a  spectral  series 
formula  for  elements  containing  several  electrons.  The  original  deriva- 
tion of  this  relation  was  purely  empirical,  but  Sommerfeld24  has  recently 
shown  that  it  possesses  some  physical  significance.  We  note  from  Ta- 
ble III  that  the  alkalis  have  one  outer  electron.  As  an  approximation 
Sommerfeld  assumed  that  all  the  other  electrons  could  be  considered 
to  be  in  a  single  circular  orbit.  In  general  then  we  assume  a  core  of 
positive  charge  Ze  surrounded  by  a  circular  ring  of  radius  ao  containing 
p  =  Z  —  k  electrons,  in  turn  surrounded  by  the  coplanar,  and  in  general 
elliptical,  orbits  of  the  single  remaining  electron.  The  outer  electron  is 
responsible  for  the  emission  pf  the  ordinary  spectral  lines.  Such  an 
atom  resembles  the  simple  structure  for  hydrogen  except  that  the  outer 
electron  is  no  longer  in  a  Coulomb  field,  on  account  of  the  disturbing 
action  of  the  ring  of  electrons.  In  assuming  elliptical  orbits  we  intro- 
duce two  degrees  of  freedom,  requiring  as  in  the  general  case  for  hydro- 
gen, the  application  twice  of  the  quantizing  integral  J*pdq  =  nh. 
The  ring  of  electrons  may  be  considered  as  a  ring  of  uniform  distribution 
of  charge  of  total  value  —  (Z  —  k)e,  and  of  radius  a0.  We  desire  the 
total  energy  Wnanr  of  the  electron  in  the  orbit  having  as  azimuthal  and 

""Atombau." 

«  "  Atombau."  2d  ed.,  Appendixes. 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         33 

radial  quantum  numbers  the  integers  na  and  nr  respectively  and  radius 
vector  of  length  r.  This  is  equal  to  the  sum  of  the  potential  energy  EP 
and  the  kinetic  energy  T  for  the  same  orbit.  We  find: 

*,--£+g+3+...,  -      (25) 

where          ci  =  j  \Z  —  k  J  ezaQ2  and  c%  =  ^j  [Z  —  k  J  e2a04  ,  (26) 


Applying  the  first  quantizing  integral: 

r2" 
J      pifc  =  2  irpt  =  naft.  (28) 


Substituting  this  value  of  p^  in  (27),  adding  (27)  and  (25),  equating 
to  the  total  energy  W,  and  solving  for  pr  we  obtain  for  the  second  quantiz- 
ing process  : 


2  rafce2       1  n2/i2      2  mci      2  mc2  ,  ,       /onN 

—  --  -2^2  —53  ---  7S-dr  =  nrh.    (29) 

This  complicated  integral,  evaluated  over  a  complete  period,  gives: 

JVftcfc2 

nn  W\2>  (30) 

- 


The  constants  a  and  a  in  this  equation  are  complicated,  but  to 
terms  of  the  first  order  are  as  follows: 


_  (2 

»« 


a  =  -  3  (2'^'~1*  •  (32) 

' 

Putting,  as  heretofore,  the  difference  in  total  energies  of  two  orbits 
Wnanr  and  Wn>an,r  equal  to  he  times  the  wave  number  of  the  emitted 
radiation  we  obtain  the  following  spectral  series  formula. 
1 


v  = 


f  +  fl  _  ac(w>  a)]2  J  •  (33) 


m  =  na-\-  nn  (m,  a)  —  W—  /he. 

This  is  the  familiar  Ritz  equation,  originally  derived  empirically. 


34  ORIGIN  OF  SPECTRA 

APPLICATION  OF  THE  RITZ  EQUATION 

There  are  four  important  series  in  the  arc  spectra  of  the  alkalis 
known  as  the  Principal,  1st  Subordinate,  2d  Subordinate  and  Berg- 
mann  Series.  Developed  empirically  these  series  are  represented  as 
follows,  where  s,  o-,  p,  IT,  d,  6,  b  and  |8  are  constants. 

Principal  : 

N  N 


K  +  s  +  <r«  s)]2       [m  +  p  +  TrK  p)]2 

m'  =1,    m  =  2,  3,  4,  etc. 
1st  Subordinate: 

*  N  (35) 


[m'  +  p  +  Tr(m',p)]2      [m  +  d  +  «(w,  d)]2 

m'  =  2,     m  =  3,  4,  5,  etc. 
2d  Subordinate : 

V  =  K  +  P  +  7r«p)]2  ~  [m  +  s  +  <r(m,s)]2  ' 

m'  =  2,     m  =  2,  3,  4,  etc. 
Bergmann : 

AT  AT 

(37) 


d)]2      [m  +  6  +  0(w,  6)]2 
7«r  =  3     m  =  4,  5,  6,  etc. 

The  first  term  in  each  of  the  above  formulae  has  a  fixed  value  of  m' 
and  is  accordingly  constant.  In  shorthand  notation  these  series  rela- 
tions may  be  written: 

Principal  v  =  1  s  -  mp,  m  =  2,  3,  4  (38) 

1st  Subordinate  v  =  2  p  -  md,  m  =  3,  4,  5  (39) 

2d  Subordinate  v  =  2  p  -  ms,  m  =  2,  3,  4  (40) 

Bergmann  i/  =  3  d  —  ?^6,  m  =  4.  5,  6  (41) 

On  comparing  Equations  (34)  to  (37)  with  Equation  (33)  we  identify 
a  successively  with  the  constants  s,  p,  d  and  b  and  —  ac  with  the  con- 
stants <T,  TT,  5  and  ]8.  By  definition  of  k  we  have  A;  =  1  for  the  alkalis. 
Referring  to  Equation  (31)  we  note  that  a  is  proportional  to  l/na3,  i.e. 
a  function  of  the  azimuthal  but  not  of  the  radial  quantum  number. 
Hence  in  order  that  a  =  s  be  a  constant  for  all  the  ms  terms,  such  terms 
must  be  characterized  by  a  constant  azimuthal  quantum  number,  the 
variation  in  m  =  na  +  nr  being  due  to  the  radial  quantum  number  alone. 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         35 

Similar  conclusions  are  necessary  for  the  mp,  md  and  mb  terms.  These 
conclusions  are  again  substantiated  by  the  fact  that  a  in  Equation  (32) 
likewise  is  a  function  of  na  but  not  of  the  variable  nr. 

Equation  (34)  shows  that  the  lowest  value 25  of  m  for  the  ms  terms 
is  1.  Since  m  =  I  =  na  +  nr,  and  since  na  j£  0  because  this  gives  the 
impossible  rectilinear  vibration  through  the  nucleus,  we  conclude  that 
na  =  1  for  all  ms  terms.  All  the  ms  terms  are  therefore  characterized 
by  an  azimuthal  quantum  number  1  and  by  a  radial  quantum  number 
from  0  to  oo .  The  principal  series  involves  combinations  of  ms  and  mp 
terms.  By  the  Bohr  principle  of  selection  the  azimuthal  quantum  num- 
ber na  may  change  by  only  +  1  or  —  1.  Hence  in  the  transition  from 
the  mp  orbit  to  the  ms  orbit,  since  na  cannot  be  zero,  the  electron  must 
go  from  an  orbit  where  na  =  2  to  an  orbit  where  na  —  1.  All  mp  orbits 
are  therefore  characterized  by  an  azimuthal  quantum  number  2  and 
by  a  radial  quantum  number  from  0  to  oo  . 

We  see  accordingly  a  common  property  in  that  the  radial  quantum 
numbers  for  both  terms  may  assume  any  positive  integral  value  includ- 
ing zero,  the  latter  value  referring  to  a  circular  orbit.  The  minimum 
value  of  m  for  the  md  terms  is  3  and  for  the  mb  terms  4.  Hence  if  these 
terms  likewise  refer  to  circular  orbits,  that  is  if  nr  can  become  zero,  we  may 
conclude  that  all  md  terms  are  associated  with  the  constant  azimuthal 
quantum  number  3  and  the  mb  terms  with  the  azimuthal  number  4- 
These  conclusions  are  summarized  in  Table  IV. 


TABLE   IV 
AZIMUTHAL  AND  RADIAL  QUANTUM  NUMBERS 


Variable  Term 

Quantum  Number 

Azimuthal 

Radial 

ms 

1 
2 
3 
4 

Oto  oo 
0  to  oo 
Oto  oo 
Oto  oo 

mp 

md  

mb 

It  is  now  seen  why  series  of  the  type  given  by  Equations  (38)  to  (41) 
should  predominate  and  not  other  combinations.  The  old  Ritz  princi- 
ple of  combination  stated  that  any  pair  of  series  terms  could  be  used  in 

25  Obviously  in  discussing  numerical  values  of  series  terms,  the  symbols  m  and  m',  which 
respectively  distinguish  initial  and  final  states,  are  interchangeable:  thus  2s  =  2's. 


36  ORIGIN  OF  SPECTRA 

combination  to  give  a  spectral  line.  We  now  associate  a  definite  azimu- 
thal  quantum  number  with  each  of  the  s,  p,  d  and  b  terms  and  by  the 
Bohr  principle  of  selection  only  such  combinations  may  occur  for  which 
na  —  —  1  or  +  1.  Hence  we  should  not  expect  lines  such  as  v  —  m's 
—  nib  since  these  involve  a  change  of  three  units  in  the  azimuthal  quan- 
tum number.  The  change  in  azimuthal  quantum  number  for  each  of  the 
four  series,  Equations  (38)  to  (41),  is  Ana  =  ±  1.  Since  the  minimum 
value  of  na  +  nr  occurs  when  nr  =  0,  we  see  why  these  four  series  begin 
with  peculiar,  fixed  values  of  m,  the  minimum  or  initial  value  being 
determined  by  the  azimuthal  quantum  number  associated  with  the 
variable  term  (except  for  the  2d  subordinate  series  where  mmin  — 
na  +  nr  =  1  +  D. 

Exceptions  to  these  deductions  may  be  found.  A  similar  excep- 
tion has  been  noted  with  helium  where  certain  components  for  which 
Ana  =  2  appear  in  a  high  voltage  discharge.  Thus  with  the  alkalis  we 
find  lines  such  as  v  =  2  p  —  mp,  Is  —  ms,  3  d  —  md  for  which  the 
change  in  azimuthal  quantum  number  is  zero.  This  fact,  however, 
would  not  be  contradictory  to  the  less  restricted  Rubinowicz  principle  of 
selection.  A  more  serious  exception  occurs  in  such  lines  as  v  =  Is  —  md 
where  the  change  in  azimuthal  quantum  number  is  two  units.  All  of 
these  exceptions  have  been,  as  with  helium,  attributed  to  the  disturbing 
effect  of  the  electrostatic  exciting  field,  under  which  condition  their 
presence  is  in  accord  with  the  theory.  Foote,  Mohler  and  Meggers,26 
on  the  other  hand  observed  1  s  —  3  d  for  sodium  and  potassium  in  a 
discharge  tube  completely  shielded  from  any  applied  field.  The  above 
conclusions  are,  however,  in  general  well  confirmed,  and  even  though 
the  theory  is  not  completely  satisfactory,  still  it  contains  much  of  great 
value  and  interest.27 

Since  we  are  concerned  in  this  book  only  with  the  more  important 
general  principles  we  are  not  able  to  extend  the  theory  to  doublet  and 
triplet  spectra,28  which  at  present  is  in  a  less  satisfactory  state  of  develop- 
ment. The  spectra  of  the  alkalis  are  characterized  by  close  doublets, 
as  for  example  the  two  D-lines  of  sodium.  The  mp  terms  are  associated 
with  double  p  orbits  pi  and  p2  of  slight  energy  difference.  Hence  the 
lines  of  the  principal  series  are  designated  by  1  s  —  mpi  and  Is  —  mp2- 
Similarly  with  the  metals  of  the  second  group  of  the  periodic  table  which 
are  characterized  by  rather  widely  separated  triplets  arising  in  the 

26  Phil.  Mag.,  43,  pp.  659-61  (1922). 

27  Probably  all  of  these  exceptions  can  be  explained  by  the  electrostatic  field  arising  in 
neighboring  atoms  and  ions. 

28  Sommerfeld,  "  Atombau,"  3d  ed.,  Chap.  6,  Section  5. 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY          37 

threefold  p  orbits,  pi,  p2  and  ps.  The  latter  family  also  has  many  single 
lines  grouped  in  series.  Single  lines  are  designated  in  the  same  notation 
except  that  capital  letters  are  used,  as  for  example  1  S  —  mP,  which 
represents  important  fundamental  lines.  We  also  find  for  these  ele- 
ments combination  series,  one  term,  belonging  to  the  single  line  group 
and  the  other  to  a  triplet  group,  as  for  example  1  S  —  mp2,  another 
fundamentally  important  series. 

FINE  STRUCTURE,  DOUBLETS  AND  TRIPLETS 

It  must  be  emphasized  that  the  fine  structure  of  hydrogen  and  of 
ionized  helium  has  nothing  in  common  with  the  fine  structure,  doublets, 
triplets,  satellites,  etc.,  of  the  more  complex  elements.  It  appears  rather 
that  the  disturbing  action  of  the  inner  groups  of  electrons  in  the  complex 
atoms  opens  out  into  several  series  what  would  otherwise  have  been  true 
fine  structure.  Or  put  conversely,  the  components  in  the  fine  structure 
of  the  Balmer  lines  of  hydrogen  are  really  terms  of  its  principal  and 
subordinate  series,  which,  because  of  the  strictly  Coulomb  field,  are  not 
widely  separated.  Thus  on  considering  the  interorbital  transitions 
involved  we  may  by  analogy  with  the  alkalis  orient  the  Balmer  lines 
as  shown  in  Table  V. 


TABLE  V 
FINE  STRUCTURE  OF  BALMER  LINES 


Line 

n 

'a-i 

-  n 

',«-« 

J+ 

* 

Series  Notation 

Ha 

2 

4. 

0 

4-3 

+ 

0 

2 

P 

-  3 

d 

1st  Sub. 

2 

+ 

0 

4-1 

+ 

2 

2 

P 

-  3 

s 

2d  Sub. 

1 

+ 

1 

4-2 

1 

2 

s 

-3 

P 

Prin. 

H, 

2 

+ 

0 

4-3 

+ 

1 

2 

p 

—  4 

1st  Sub. 

2 

+ 

0 

4-1 

+ 

3 

2 

p 

-  4 

s 

2d  Sub, 

1 

+ 

1 

4-2 

+ 

2 

2 

s 

—  4 

p 

Prin. 

etc. 

NUCLEAR  DEFECT  OF  A  RING  OF  ELECTRONS 

In  succeeding  discussions  it  is  necessary  to  consider  the  shielding 
action  on  the  nucleus  by  a  ring  of  several  electrons.  From  purely 
geometrical  considerations,  assuming  the  inverse  square  law,  it  may  be 
shown  that  the  force,  which  is  radial,  acting  on  any  one  of  n  electrons, 


38  ORIGIN  OF  SPECTRA 

symmetrically  distributed  in  a  ring,  of  radius  a0,  with  the  charge  +  Ze 
at  the  center,  is: 

Ze*        e2     *"f  '  irk  ,,ON 

=  ---        I    *>**- 


=  £2(Z-sn),  (43) 

-  t=re-l  , 

where  s»  =  I    2    cosec—-  (44) 

t-i 

The  quantity  sn  is  called  the  nuclear  defect  of  the  ring  of  n  electrons  and 
Z'  =  Z  —  s^the  "  effective"  core  charge.  For  large  values  of  n,  above 
10  to  20,  we  may  represent  sn  approximately  by  the  simple  formula: 

sn  =  £-  (nat  In  n  +  0.  12)  .  (45) 

&  7T 

The  radius  of  a  single  ring  of  n  electrons  about  a  nuclear  charge  Ze  is  as 
follows  : 

®h  &h  fAa\ 

a°  =  z^a  =  z» 

where  ah  is  the  radius  of  the  hydrogen  atom.  From  Equations  (1) 
and  (3)  we  find  for  an  azimuthal  quantum  number  1  : 

h2 


In  case  the  electrons  are  distributed  in  two  concentric  rings,  in 
accordance  with  our  interpretation  of  the  quantum  theory,  we  assign 
to  each  electron  in  the  inner  ring  one  unit  of  angular  momentum  and  to 
each  electron  in  the  outer  ring  two  units.  Hence  for  a  ring  of  radius  ai 
containing  p  electrons  and  an  outer  ring  of  radius  a2  containing  q  electrons 
we  find: 


The  total  energy  of  the  p  electrons  in  the  inner  ring  and  that  of  the  q 
electrons  in  the  second  ring  may  be  shown  to  have  the  values : 

,,,  Nhc,~  /F^v 

wp9*  -P -rr  (z  ~  SP)  >  (5°) 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY          39 

&  ~  P  ~  s«)2.  (51) 

AJ 

It  should  be  noted  in  Equations  (49)  and  (51)  that  the  inner  ring  is 
considered  to  be  sufficiently  close  to  the  nucleus  so  that,  as  far  as  the 
outer  ring  is  concerned,  its  nuclear  defect  is  p,  these  p  electrons  simply 
decreasing  the  core  charge  by  their  total  value  pe.  Similarly  in  Equa- 
tions (48)  and  (50)  the  effect  of  the  outer  ring  is  neglected.  It  is 
accordingly  evident  that  in  considering  the  orbits  of  a  single  electron 
revolving  outside  of  other  rings  of  electrons,  the  number  of  electrons  in 
the  outer  ring  is  a  predominant  factor,  the  exact  distribution  in  the  inner 
rings  being  of  minor  importance. 

SPARK  SPECTRA 

Spectral  lines  which  arise  in  ionized  atoms  are  called  enhanced  or 
spark  spectra.  Formerly  they  could  be  produced  in  the  laboratory 
only  by  high  voltage  condenser  discharge  —  whence  the  terminology 
"  spark"  spectra.  We  have  already  considered  the  enhanced  spectrum 
of  ionized  helium  and  shall  now  discuss  the  spectra  of  the  ionized  alkali 
earths.  Referring  to  Table  III,  we  note  that  the  normal  atoms  in  this 
group  all  contain  two  electrons  in  the  outer  ring.  We  shall  assume  that 
one  of  these  has  been  removed  by  the  process  of  ionization.  The  struc- 
ture then  becomes  identical  with  that  of  the  alkali  of  next  lower  atomic 
number  except  that  the  core  charge  is  one  unit  greater.  This  is  equivalent 
to  putting  kz  =  4  in  Equation  (33).  The  enhanced  spectrum  of  ionized 
magnesium,  accordingly,  should  resemble  the  arc  spectrum  of  sodium, 
and  similarly  for  the  other  pairs  of  elements  in  these  two  groups.  The 
variable  series  term  for  these  enhanced  lines  should  by  Equation  (33) 
take  the  form : 

„«  = !# (<m 

vrti  u  )       TM     i   „      I    „*       ..*„  /™    ~*MO  \y*/ 


We  note  that  since  k  =  2,  the  factor  k*N  (=  4  N  =  A)  appears  in 
the  variable  term  of  the  enhanced  spectra  instead  of  simply  N.  This 
fact  is  fairly  'well  substantiated  by  empirical  computation 29  as  shown 
in  Table  VI. 


29  Since  this  was  written,  Fowler's  book  on  "Series  in  Line  Spectra"  has  appeared.  He 
has  recomputed  these  series,  using  A  -  4N  as  predicted  by  theory.  Table  VI  is  accordingly 
of  historical  interest  only.  See  section  on  "  Spectroscopic  Tables." 


40 


ORIGIN  OF  SPECTRA 


TABLE  VI 
CONSTANT  IN  ENHANCED  SERIES  FORMULAE 


Element 

Series 

Constant  =  A 

A/N 

Me: 

1st    Sub 

423377 

3.9 

Sr  

2d    Sub. 
1st  Sub 

413202 
410836 

3.8 
3.7 

Ca  

2d    Sub. 
1st  Sub. 

415157 
423416 

3.8 
3.9 

Ba  

2d    Sub. 
1st  Sub. 

421559 
390431 

3.8 
3.6 

2d    Sub. 

397795 

3.6 

We  shall  now  discuss  the  relation  between  the  constants  a*  for 
enhanced  spectra  of  the  alkali  earths  and  the  constants  a  for  the  arc 
spectra  of  the  alkalis.  In  order  to  approximate  physical  conditions 
more  closely,  as  shown  by  Table  III,  we  shall  consider  two  rings  of  elec- 
trons about  the  core,  besides  the  orbit  of  the  valence  electron,  the  outer 
ring  of  radius  a2  containing,  according  to  Table  III,  q  =  8  electrons  and 
the  inner  ring  of  radius  a\  containing  p  =  Z  —  q  —  k  electrons.  The 
remaining  valence  electron  revolves  about  this  entire  structure.  More 
rings  could  be  assumed,  for  example  four  with  strontium,  but  as  already 
pointed  out,  these  are  unnecessary  refinements  as  far  as  the  orbits  of  the 
valence  electron  are  concerned. 

The  expression  for  a  as  derived  by  Sommerfeld  for  a  single  ring 
(radius  a0)  of  electrons  is  given  by  Equation  (31)  where  k  =  1.  The 
value  of  a*  is  likewise  determined  by  (31)  where  k  =  2.  This  relation 
involves  Ci  which  is  by  Equation  (26)  proportional  to  a20.  We  see,  how- 
ever, by  Equation  (46)  that  a0  depends  upon  the  nuclear  charge  and  hence 
is  different  for  Mg  and  Na,  and  other  corresponding  pairs  of  elements. 
This  shrinkage  of  the  ring  when  the  nuclear  charge  increases  by  one 
unit  must  be  considered  in  determining  the  ratio  a* /a.  Now  the  addi- 
tion of  a  second  ring  simply  alters  the  value  of  c\  in  Equation  (31). 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY 


41 


Taking  this  into  account  as  well  as  allowing  for  changes  in  the  radii  of 
the  two  rings  as  determined  by  Equation  (48)  we  find: 


P 


16 


(q  +  2  -  s.y 


P 


16 


(53) 


(Z  -  sp)*   '    (q  +  1  -  Sq)* 

where  Z*  =  Z  +  1  is  the  atomic  number  of  the  alkali  earth  and  Z  is 
the  atomic  number  of  the  alkali.  For  the  doublet  system  of  enhanced 
lines  we  use  precisely  the  same  formulae  Equations  (38)  to  (41)  as  for 
the  arc  spectra  of  the  alkalis  except  that  we  replace  s,  p,  d  and  6  by  the 
letters  @.  $,  $)  and  23  respectively.  Table  VII  shows  the  values  of  the 
empirically  determined  series  constants.  The  last  column  gives  the 
ratio  a* /a  computed  by  Equation  (53) .  This  agrees  with  the  empirical 
ratios,  again  substantiating  our  theory. 


TABLE  VII 

RELATION  BETWEEN  a*  AND  a 


* 

a*  -T-  a 

Elements 

a*  =  © 

a  =  s 

a*  =  9) 

a  =  p 

<5/s 

%/P 

Com- 
puted 

Mg/Na  

.93 

.65 

30 

15 

1  43 

200 

148 

Ca/K  

1.20 

.82 

.50 

.29 

1  46 

1.72 

1.49 

Sr/Rb 

1  32 

81 

61 

36 

1  63 

1  70 

1  66 

Ba/Cs  

1.43 

95 

75 

45 

1  50 

* 

1  66 

1.66 

We  may  therefore  conclude  that  in  all  detail  the  enhanced  spectrum 
of  an  alkali  earth  resembles  the  arc  spectrum  of  the  alkali  of  next  lower 
atomic  number.  This  relation  may  be  extended  to  other  pairs  of  ele- 
ments. If  we  remove  the  valence  electron  from  sodium  the  configura- 
tion is  similar  to  that  of  neon,  as  seen  from  Table  III.  Hence  the  spark 
spectrum  of  sodium  should  resemble  the  arc  spectrum  of  neon,  and 
similarly  for  the  other  pairs  of  elements  in  these  two  groups.  Such  is 
observed,  qualitatively,  to  be  the  case.  Quantitative  evidence  is  not 
at  hand,  since  the  series  relations  are  as  yet  unknown  for  the  spark 


42 


ORIGIN  OF  SPECTRA 


spectra  of  the  alkalis  and  are  not  known  at  all  completely  for  the  rare 
gases.  But  both  are  alike  in  their  complexity  of  structure.  With 
these  and  a  few  other  facts  Kossel  and  Sommerfeld30  proposed  a  general 
''displacement  law"  for  spectra  as  summarized  in  Table  VIII. 

TABLE  VIII 

RELATION  OF  ARC  AND  SPARK  SPECTRA 


Group 

VIII,  0 

I 

II 

III 

IV 

V 

VI 

VII 

Arc.... 
Spark.  . 

complex 
and 
triplets 
? 

doublet 

complex 
(and 
triplets?) 

triplet 
doublet 

doublet 
triplet 

triplet? 
doublet? 

doublet? 
triplet? 

triplet 
doublet9 

? 

triplet? 

Where  a  question  mark  appears,  the  series  relations  have  not  been  as  yet 
untangled  in  the  maze  of  spectral  lines.  The  displacement  law  states 
that  the  spark  spectrum  of  any  simply  ionized  element  resembles  the 
arc  spectrum  of  the  element  of  next  lower  atomic  number. 

If  an  element  loses  two  electrons  its  spectrum  should  be  similar 
to  the  arc  spectrum  of  the  element  of  second  lower  atomic  number. 
There  is  some  indication  of  this  second  type  of  enhanced  spectra  in  the 
spark  spectra  of  carbon  and' of  silicon,  but  nothing  definite  has  been  as 
yet  established.  The  doubly  ionized  lithium  atom  should  give  a  spec- 
trum identical  to  hydrogen  except  that  the  important  lines  should  lie  in 
the  extreme  ultra-violet.  The  wave  numbers  should  obey  the  approxi- 
mate relation,  analogous  to  Equation  (9) : 

v  —  q  AT 

v  -  y/v 

The  series  for  which  n'  —  1,  converges  at  9  N  or  about  X  101  A,  a  spectral 
region  of  soft  x-rays.  Lines  in  series  for  higher  values  of  n',  which  lie 
in  the  neighborhood  of  the  visible  spectrum,  have  at  times  been  thought 
to  have  been  detected  in  stellar  spectra,  but  the  evidence  is  not  conclu- 
sive. 

The  spectrum  of  a  negatively  charged  atom,  one  which  has  attached 
an  extra  electron,  should  resemble  the  arc  spectrum  of  the  element  of 
next  higher  atomic  number. 


so  Kossel  and  Sommerfeld,  Verh.  d.  Phys.  Ges.,  21,  pp.  240-59  (1919). 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY          43 

From  the  foregoing  discussion  it  appears  that  the  behavior  of  the 
elements  as  regards  their  spectra  is  analogous  to  that  in  radioactive 
transformations  where  the  emission  of  an  alpha  particle  gives  rise  to  an 
element  two  steps  to  the  left  in  the  periodic  table  and  the  emission  of  a 
beta  particle,  an  element  one  step  to  the  right. 

SPECTROSCOPIC  TABLES 

Until  recently  there  have  been  but  three  tables  of  wave-lengths 
available  in  which  the  lines  have  been  correlated  in  series  according 
to  formulae  of  the  Ritz  or  similar  type;  that  of  Dunz,31  a  supplement  to 
Dunz's  tables  prepared  by  Lorenser32  and  these  same  tables  arranged 
with  a  different  notation  in  a  book  by  Konen.33  In  these  tables  the 
numerical  values  of  all  the  variable  terms  in  series  formulae  are  con- 
veniently tabulated. 

The  notation  employed  by  Dunz  and  Lorenser  is  that  of  Paschen. 
Paschen  originally  proposed  for  all  the  ms  terms,  half  integer  values  for 
m  such  as  1.5  s,  2.5  s  etc.  Later  it  was  found  that  the  J  possessed  no 
physical  significance  and  hence  more  recent  writers  have  included  this 
factor  in  the  series  constant  a  of  Equation  (33).  Whole  numbers  are 
therefore  assigned  to  na  +  nr  =  m,  viz.  I  s,  2  s  etc.,  just  as  has  been 
always  done  with  the  mp  and  other  variable  terms.  Also  the  variable 
term  mAp  used  by  earlier  writers  for  the  Bergmann  series  has  been 
changed  to  mb.  Accordingly  the  only  modification  necessary  to  the 
tables  of  Dunz  and  Lorenser,  excluding  errors,  is  the  subtraction  of  J 
from  each  value  of  m  which  refers  to  a  ms  or  mS  term  and  the  substitu- 
tion of  mb  for  raAp.  However,  since  these  tables  were  printed  much  more 
precise  spectroscopic  data  have  become  available,  especially  in  enhanced 
spectra  which  have  been  materially  revised,  and  the  entire  subject  has 
been  brought  up  to  the  date  April,  1921,  by  Fowler34  in  a  book  of  nearly 
200  pages,  published  March,  1922. 

The  vast  quantity  of  data  in  this  book  was  computed  before  the 
physical  significance  of  the  revised  Paschen  notation  was  appreciated. 
A  notation  is  employed  which  is  just  enough  different  from  the  now 
generally  preferred  notation  to  be  confusing  to  the  beginner  in  this 
subject.  The  following  table  lists  the  essential  differences  between  the 
revised  Paschen  notation  which  is  employed  in  this  book  and  Fowler's 
notation.  One  should  familiarize  himself  with  both  notations;  with 
the  first  in  order  to  appreciate  the  physical  significance  on  the  basis  of 

31  Dunz,  Tubingen  Dissertation,  1911. 

32  Lorenser,  Tubingen  Dissertation,  1913. 

33  Konen,  "Das  Leuchten  der  Gase  und  Dampfe. " 

34  See  general  reference  5  at  end  of  chapter. 


44 


ORIGIN  OF  SPECTRA 


Sommerfelpl's  interpretation,  with  the  second  in  order  to  obtain  readily 
the  numerical  values  from  Fowler's  tables. 


Revised  Paschen  Notation 

Fowler 

Notation 

1 

5, 

2 

S 

1 

S 

2 

S 

2P, 

3 

P 

1 

p 

,    2 

P 

3 

D. 

4 

D 

2D 

,   3 

D 

1 

s, 

2 

s 

1 

s, 

2 

s 

or 

I'f. 

2(7 

2 

P» 

3 

P 

1 

2 

P 

or 

ITT, 

2-7T        ' 

3 

d, 

4 

d 

2 

£ 

3 

d 

or 

26, 

35 

4 

5 

5 

b 

3 

*/  ? 

4 

f 

or 

o  (p« 

4  <f> 

1 

®> 

2 

(5 

1 

2 

<T 

2 

ro 

3 

? 

1 

7T, 

2 

7T 

3 

^ 

4 

5) 

26, 

3 

6 

4 

», 

5 

33 

3 

<t> 

4 

4> 

In  Fowler's  notation,  singlet,  doublet  and  triplet  series  are  dis- 
tinguished respectively  by  capital,  Greek  and  small  letter  abbreviations. 
The  ordinal  numeral  m,  however,  may  be  different  from  that  in  the  revised 
Paschen  notation.  The  following  examples  serve  as  illustrations. 


Series 


Notation 


Revised  Paschen 


Fowler 


Principal  series  of  doublets  of  alkalis 

1st  subordinate   (diffuse)  series   of 
doublets  of  alkalis 

2d  subordinate    (sharp)   series    of 
doublets  of  alkalis 


Bergmann   (fundamental)   series  of 
doublets  of  alkalis .... 


Principal  series  of  triplets  of  alkali 
earths 

1st  subordinate  series  of  triplets  of 
alkali  earths 

2d  subordinate  series  of  triplets  of 
alkali  earths 

Principal  series  of  singlets  of  alkali 
earths , 


Combination  series  of  singlets  of  al- 
kali earths 

Principal  series  of  doublets  of  ionized 
alkali  earths. . 


1st  subordinate  series  of  doublets  of 
ionized  alkali  earths 

2d  subordinate  series  of  doublets  of 
ionized  alkali  earths . . . 


Is  —  mp,  m  =  2,  3 

2  p  —  md,  m  =  3,  4 

2  p  —  ms,  m  =  2,  3 

3d  —  w6,  m  =  4,  5 

Is  —  mp,  m  =  3,  4 

2  p  —  md,  m  =  3,  4 

2  p  —  ms,  m  =  1,  2 

1  £  —  mP,  m  =  2,  3 

1  /S  —  mpa,  m  =  2,  3 

1  ©  -  m9>,  m  =  2,  3 

2  9)  -  m£,  m  =  3,  4 
2  9)  —  m©,  m  =  2,  3 


Iff 

I  7T 

ITT 
25 
Is 
lp 
Ip 
IS 
IS 
Iff 
ITT 
ITT 


mir,    m 

•  md,     m 

•  mff,    m 
m  <f>,   m 
mp,     m 
md,    m 
ms,     m 

•  mP,  m 
mp2,  m 
mw,    m 
md,     m 
mff,    m 


1,2 
2,3 
2,3 
3,4 
2,3 
2,3 
1,2 
1,2 
1,2 
1,2 
2,3 
2,3 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         45 

These  are  merely  some  of  the  more  striking  differences  in  the  nota- 
tions. For  the  minor  differences  in  the  many  combination  series,  refer- 
ence must  be  made  to  the  original  tables.  Throughout  this  book  we 
shall  refer  to  fundamental  lines  as  those  belonging  to  series  converging 
at  1  s,  1  S  or  1  @.  They  are  lines  concerned  with  interorbital  transitions 
for  which  one  orbit  represents  the  normal  state  of  the  unexcited  atom. 
They  are  accordingly  fundamentally  important  lines  from  the  standpoint 
of  atomic  structure.  Fowler  and  some  other  English  and  American 
writers  use  the  term  "  fundamental"  in  reference  to  what  we  have  called, 
following  the  German  custom,  the  Bergmann  series.  While  the  latter 
nomenclature  undoubtedly  gives  unwarranted  credit  to  Bergmann  it  is 
preferred  to  the  nomenclature  "  fundamental,"  since  physically  this 
series  is  quite  remote  from  fundamental. 

In  the  computation  of  series  limits  and  variable  terms  Fowler  em- 
ploys the  Hicks  instead  of  the  Ritz  formula  as  follows : 

,  N 

K  O)  —jTT2  '  (A) 


Referring  to  Equations  (33)  to  (37),  the  variable  term  of  the  Ritz  formula 
takes  the  form 


Carrying  out  the  expansion  involved  by  (m,  a)  in  the  denominator  and 
dropping  terms  beyond  m  which  are  relatively  small,  especially  when  m 
is  large,  we  obtain: 

(*•«>-  —      _NacNf-  (C) 


On  comparing  this  to  (A)  we  note  that  since  in  (A)  the  ordinal  number  m 
occurs  as  the  first  power  in  the  third  term  of  the  denominator  while  in 
(C)  it  occurs  as  the  square,  a'  is  not  identical  with  acN  and  a  may  differ 
somewhat  from  a'. 

Since  Fowler  also  uses  different  values  of  m,  the  numerical  values  of 
all  variable  series  terms  (m,  a)  will  be  very  slightly  different  when  com- 
puted by  the  two  formulae.  Fortunately  the  third  term  in  the  de- 
nominator is  small,  a  correction  term,  so  that  these  discrepancies  are  of 
little  importance.  A  series  line  is  always  made  up  of  the  difference  of 
two  terms  and  is  so  computed  that  the  difference  is  practically  the  same 
with  each  system  of  notation,  since  it  must  give  the  observed  line.  Limits 


46  ORIGIN  OF  SPECTRA 

however  are  not  observed,  but  are  computed  values,  and  accordingly 
depend  somewhat  upon  the  type  of  formula  chosen.  We  may  therefore 
expect  to  find  small  differences  in  series  limits  in  tables  computed  in 
different  manners.  While  these  computed  frequencies  may  be  known  to 
six  significant  figures  on  the  basis  of  a  specified  formula,  different  formulae 
may  disagree  in  the  fifth  figure  or  to  even  10  parts  in  50,000,  and  in 
certain  cases  where  but  few  series  terms  are  known,  the  differences 
may  be  very  much  greater. 

In  this  book  we  are  not  concerned  with  computation  of  series  limits 
but  as  will  appear  later  we  are  interested  in  the  actual  physical  value 
of  convergence  wave  numbers  regardless  of  the  method  whereby  they 
are  obtained.  From  this  standpoint  many  of  the  limits  listed  in  our 
tables  are  probably  not  certain  by  ten  units.  However,  this  small  un- 
certainty is  of  negligible  significance  when  referred  to  ionization  po- 
tentials, energy  levels  in  the  atom,  etc.35 

In  applying  deductions  from  the  theoretical  derivation  of  the  Ritz 
equation  to  values  of  the  spectral  series  constants  a  and  ac  of  Equation 
(B)  as  was  done  for  example  in  Table  VII,  one  should  use  the  constants 
determined  by  the  Ritz  rather  than  by  the  Hicks  equation.  Even  here 
however  the  differences  are  usually  trivial  when  one  considers  that  the 
theory  in  its  present  state  is  only  qualitatively  verified. 

X-RAYS 

One  of  the  greatest  successes  of  the  quantum  theory  of  spectroscopy 
is  its  application  to  the  interpretation  of  x-ray  spectra.36  The  char- 
acteristic x-ray  spectra  of  an  element  may  be  grouped  in  series  designated 
as  the  K,  L,  M,  etc.,  series.  The  K  radiation,  which  is  of  the  shortest 
wave-length,  is  produced  by  an  interorbital  transfer  where  the  final 
orbit  is  the  inmost  one  in  the  atom.  Figure  3  shows  schematically  how 
the  various  prominent  x-ray  lines  are  excited.  Ka,  the  line  of  longest 
wave-length  in  the  K  series,  is  produced  by  an  electron  falling  from  the 
L  ring  to  the  K  ring.  La,  the  line  of  longest  wave-length  in  the  L 
series,  is  produced  by  an  electron  falling  from  the  M  ring  to  the  L  ring. 
The  second  line  of  the  K  series,  K&,  arises  in  a  transition  between  the 
M  and  K  rings.  The  limit  of  any  series  is  the  frequency  determined 
by  an  electron  falling  from  outside  the  atom  into  a  vacant  space  in  the 

35  Inconsistencies  between  the  data  given  in  the  illustrations  and  tables,  in  this  book, 
amounting  to  5  or  less  units,  may  occur  occasionally,  since  the  latter  have  been  revised  in  the 
proof  to  fit  the  latest  available  figures.    These  differences,  however,  are  of  little  significance. 

36  See  Chapter  IX  for  detailed  discussion. 


THE  QUANTUM   THEORY  OF  SPECTROSCOPY         47 

corresponding  ring.  Since,  as  seen  from  Table  III,  the  inner  rings  con- 
cerned with  the  production  of  x-rays  all  contain  several  electrons,  the 
spectral  series  relations  cannot  be  given  by  a  simple  formula  of  the 
Balmer  type.  It  is  necessary  to  consider  the  modifying  effect  of  the 
other  electrons  in  the  various  rings. 


M 


Limit 

FIG.  3.     Simple  diagram  showing  prominent  x-ray  lines. 

The  Ka  line,  for  elements  of  atomic  number  10  or  greater,  is  probably 
the  result  of  an  interorbital  transition  represented  as  follows,  where  the 
figures  and  letters  denote  numbers  of  electrons  in  the  groups  specified 

K-r'mg  L-ring          M-ring 

initial  condition  1  8  r 

final  condition  2  7  r 

By  aid  of  Equations  (50)  and  (51)  we  shall  compute  the  total  energy  of 
the  rings  in  the  initial  and  in  the  final  conditions. 

Initial  Condition:      Wp  =  -  NhcZ\  (54) 

Wq  =  -  2Nhc(Z  -  3.80)2,  (55) 

rNhc 


Wr=  - 


(56) 


48 


ORIGIN  OF  SPECTRA 


Final  Condition:       Wp  =  -  2Nhc(Z  -  0.25)2, 

Wq  =  -  l.75Nhc(Z  -  4.30)2, 

WT=   -£ 


(57) 
(58) 

(59) 

Subtracting  the  value  of  the  total  final  energy  from  that  of  the  total 
initial  energy  and  equating  this  to  hcv  we  obtain : 

For  Ka  i  =  Z2  (p  -  i)  -  0.85  Z  +  3.6.  (60) 

The  first  term  in  this  expression  is  the  simple  formula  representing  the 
transition  of  an  electron  from  orbit  2  to  orbit  1,  analogous  to  Equation 
(6)  for  hydrogen.  The  second  and  third  terms  are  due  to  the  disturbing 
action  of  the  other  electrons.  While  a  formula  derived  in  the  above 
manner  is  of  great  interest  if  in  only  qualitative  agreement  with  experi- 
ment, unfortunately  this  equation  leaves  much  to  be  desired  from  the 
quantitative  standpoint.  The  introduction  of  relativity  considerations 
does  not  alter  materially  the  computations  for  elements  of  low  atomic 
number  and  the  effect,  here  neglected,  of  the  electrons  in  the  outer 
rings  on  the  energy  of  the  inner  rings,  is  also  of  a  small  order  of 
magnitude.  It  is  of  interest  to  note  that  if  in  Equation  (57)  instead  of 
sp  =  0.25  we  arbitrarily  put  sp  =  0.45  we  obtain : 


For  Ka  jj  =  Z*  0*  ~  &)  ~  1'65  Z  +  3'88'  (61) 

This  relation  agrees  excellently  with  experiment  as  shown  by  Table  IX. 

TABLE  IX 

COMPUTATION  OF  v/N  FOB  THE  LINE  Ka  FOB  ELEMENTS   OF  Low 

ATOMIC  NUMBEB 


Element 

Z 

Computed  v/N 

Observed  v/N 

Na.  . 

11 

76.5 

76.6 

Mg.. 

12 

92.1 

92.0 

Al        

13 

109.2 

109.3 

Si 

14 

127.8 

1280 

P  

15 

147.9 

148.0 

s  

16 

169.5 

170.0 

Cl  

17 

192.6 

193.4 

K 

19 

243.3 

243.8 

Ca 

20 

270.9 

271.3 

THE  QUANTUM   THEORY  OF  SPECTROSCOPY         49 

Just  as  is  the  case  with  hydrogen  and  ionized  helium  where  we  find 
each  line  made  up  of  several  components,  so  with  x-rays.  Instead  of  the 
simple  structure  schematically  indicated  by  Figure  3,  many  other  x-ray 
lines  are  observed.  A  two-quantum  L  electron  may  move  in  either  a 
circle  or  an  ellipse.  Likewise  the  M  orbits  of  quantum  number  three 
may  be  either  a  circle  or  two  types  of  ellipses.  Hence  we  obtain  doublet 
separations  in  the  K  and  L  spectra,  due  to  the  two  forms  of  L  orbits. 
The  fine  structure  of  x-ray  lines,  which  is  still  more  complicated  than 
that  just  indicated,  will  be  described  in  detail  in  Chapter  IX.  It  is 
of  interest  here  merely  to  mention  the  Sommerfeld  derivation  of  the 
magnitude  of  the  L-doublet  separation  as  obtained,  from  relativity 
considerations.  The  method  is  analogous  to  that  used  in  deriving 
Equation  (24)  for  the  hydrogen  doublet.  Employing  Equation  (20) 
we  compute  the  energy  of  a  single  electron  for  the  orbit  na  +  nr  =  1  +  1 
and  for  the  orbit  na  +  nr  =  2  +  0.  The  difference  in  these  energies  is 
equal  to  hckv.  One  point  must  be  noted,  however,  in  that  instead  of 
the  atomic  number  Z,  we  use  Z'  =  Z  —  z.  This  is  simply  another 
method  of  correcting  for  the  effect  of  the  other  electrons  in  the  atom. 
For  most  of  the  elements  z  =  3.50,  empirically  determined,  but  it  is 
evident  that  this  is  only  an  approximate  method  for  representing  nuclear 
defect  and  cannot  be  applied  to  elements  of  very  low  atomic  number. 

We  accordingly  obtain  from  Equation  (20)  the  following  relation 
in  which  the  development  is  carried  as  far  as  the  sixth  power  of  the 
constant  a. 


A,  =  ATZ'«l  +        z'»  +        -+  .  .  .    .  (62) 


Replacing  Na2  by  16  AJ>H,  Equation  (24),  we  may  compute  the  L-doub- 
let separation  for  any  element  in  terms  of  the  separation  of  the  hydro- 
gen doublet.  As  an  example,  for  uranium,  Zf  =  92  —  3.50,  we  find 

A^  =  8.17  •  107  AvH  =  2.98  •  107  cm-1. 

The  observed  doublet  separation  for  uranium  is  3.02  •  107  cm"1,  in  excellent 
agreement  with  the  above  computed  value  which  represents  an  extra- 
polation of  eighty  million-fold.  We  here  see  that  the  fine  structure  of 
the  hydrogen  Balmer  lines  is  carried  throughout  the  entire  range  of 
elements,  appearing  in  their  K  and  L  x-ray  spectra,  on  an  increasingly 
greater  scale  of  magnification  as  the  atomic  number  progresses. 


50 


ORIGIN  OF  SPECTRA 


GENERAL  REFERENCES 

(1)  Bohr,  Phil.  Mag.,  26,  pp.  1,  476,  857  (1913);  idem.,  27,  p.  506  (1914);  idem., 
29,  p.  332  (1915);  idem.,  30,  p.  394  (1915). 

(2)  Bohr,  The  Quantum  Theory  of  Line  Spectra,  Parts  I  and  II,  Danish  Academy 
of  Science,  100  pp.  (in  English). 

Series  Spectra  of  the  Elements,  Zeit.  Physik,  2,  pp.  422-69  (1920). 
Structure  of  Atoms  and  the  Physical  and  Chemical  Properties  of  the  Elements, 
Zeit.  Physik,  9,  pp.  1-67  (1922). 

(3)  Sommerfeld,  Atomic  Structure  and  Spectral  Lines,  3d  Edition,  764  pp.  (1922). 

(4)  Silberstein,  Report  on  the  Quantum  Theory  of  Spectra,  42  pp.   (1920).     A 
splendid  synopsis  of  the  theoretical  development  to  this  date. 

(5)  Fowler,  Report  on  Series  in  Line  Spectra,  183  pp.  (1922).     The  most  com- 
prehensive catalog  of  series  spectra  ever  published. 

(6)  Adams.     The  Quantum  Theory,  Bull.  Nat.  Res.  Coun.,  1,  pp.  301-81    (1920). 

(7)  Page,    Dynamic   Theories   of   Atomic  Structure,  Bull.  Nat.  Res.  Coun.,  2, 
pp.  356-95  (1921). 


Chapter  II 
Energy  Diagrams 

It  is  convenient  to  represent  the  various  stationary  states  of  a 
radiating  atom  by  schematic  diagrams.  For"  example,  in  the  case  of 
hydrogen  the  total  energy  of  the  atom  is  a  minimum  when  the  electron 
is  in  the  inmost  orbit,  total  quantum  number  1,  as  is  evident  from 
Equations  (3),  (17)  or  (20).  When  the  electron  is  displaced  to  infinity, 
or  just  outside  the  sphere  of  influence  of  the  core,  which  practically  is  a 
very  small  distance,  the  total  energy  is  all  potential  and  is  a  maximum. 
Between  these  two  positions  we  have  many  orbits  where  the  electron 
assumes  intermediate  values  of  the  total  energy  corresponding  to  the 
total  quantum  numbers  n  =  2,  3,  4,  etc.  In  general  it  is  more  con- 
venient to  consider  instead  of  the  total  energy  of  the  electron,  the  amount 
of  work  required  to  displace  it  from  an  inner  to  an  outer  orbit.  Hence 
to  the  inmost  orbit  is  ascribed  the  largest  numerical  value  of  the  work, 
this  being  the  work  necessary  to  displace  the  electron  to  infinity.  Such 
a  diagram  for  hydrogen  is  shown  in  Figure  4.  The  first  orbit,  n  =  1, 
corresponds  to  215.6  X  10~13  ergs;  the  second  to  53.9;  the  third  to  23.95, 
etc.  That  is,  it  requires  215.6  X  10 ~13  ergs  to  completely  remove  the 
electron  from  its  inmost  stable  position  in  the  hydrogen  atom,  and  53.9 
X  10~13  ergs  to  remove  it  from  the  second  orbit,  etc.  The  various 
series  lines  of  hydrogen  are  shown  on  this  diagram.  For  example  Ha 
represents  a  transition  from  orbit  3  to  orbit  2.  Referring  to  the  energy 
scale  on  the  right  we  accordingly  find  that  this  represents  an  energy 
change  of  3  X  10" 12  ergs.  (This  value  is  obtained  by  taking  the  differ- 
ence between  the  energy  values  corresponding  to  the  head  and  tail  of 
the  arrow  marked  a.  Note  that  logarithms  of  energy  are  plotted  on  the 
left  in  order  to  obtain  an  open  scale.)  Similarly  the  energy  required  to 
produce  an  emission  of  one  quantum  of  any  frequency  represented  by 
'the  series  lines  of  hydrogen  may  be  read  from  this  plot.  On  the  com- 
pressed scale  of  the  diagram  the  fine  structure  of  the  various  lines  is  not 
indicated.  Actually  orbit  2  is  double  and  orbit  3  triple,  as  explained 
earlier  in  the  text,  cf.  page  27. 

51 


52 


ORIGIN  OF  SPECTRA 


Usually  in  such  diagrams  we  are  more  concerned  with  the  wave 
number  v  of  the  radiation.  It  is  accordingly  desirable  to  plot  instead 
of  log  energy  the  equivalent  value  of  log  v.  In  this  case  the  difference 


-  oo 

!°°     ErgsxlO13 

0.6 
0.8 
1.0 

r-i 

__ 

i 
i 

n                       ^    rrrt 

W 
0 

•  >—  ' 
J_) 

co 

0Fi    OO 

( 

! 

(4                   i^.WW 

C 

+ 

- 

1 
"i 

/ 

fi    - 

- 

/ 

$ 

u 
o 

X 

&1.4 

L 

2 

— 

Paschen 

X3 

0) 

a 

^ 

be 

C 

J  !-6 

1.8 

™ 

E 

3 

2c       R*7  on 

- 

Balmer 

3 

Or 

2.0 

- 

1 
efl 

c- 

o 

00 

> 
2 

2.2 
2.4 

~ 

1 

1         jMR  fin 

2 

Lyman 

FIG.  4.     Energy  diagram  for  hydrogen. 

in  wave  numbers  corresponding  to  the  initial  and  final  orbits  gives  di- 
rectly the  wave  number  of  the  emitted  radiation.  Such  a  diagram  for 
sodium  is  shown  in  Figure  5.  All  of  the  p-orbits  are  really  double,  but 
their  separation  is  indistinguishable  on  this  small  scale  of  wave  numbers. 


ENERGY  DIAGRAMS 


53 


Each  D-line  is  represented  by  a  transition  from  the  initial  2  p  orbit 
to  the  final  1  s  orbit,  and  its  wave  number  is  given  by  the  difference 
in  wave  numbers  corresponding  to  these  two  energy  levels  24472  or 
24489  to  41449.  Similarly  for  all  other  lines  as  far  as  shown  on  the 


-                                                                               4149 

4386 

4412 

^  7 

5074 

6403 

6859 

_ 

6897 

3.9 

8248 

4.0 

— 

en 

T—  > 

11,175 

;> 

12,274 

4.1 

C\J 

in 

4.2 

15,706 

c 

0 

4.3 

— 

£ 

0 

t 

24,472 

4.4 

*"* 

B 

s 

24,489 

4.5 

- 

1 
S 

»  11    1?    If          1 

•    <go,  .    Si.      *4                o 

0 

£ 

t-H                     O3                       n 

3       f^                       J 

J)  tO                                           m 

4.6 

- 

0, 

?-i                 co               0 

^        41,449             n 

(SI 

FIG.  5.     Schematic  representation  of  the  arc  spectrum  of  sodium. 


5p 

5b 
5d 

4s 


4p 
4b 
4d 

3s 


3p 
3d 


2s 


2p 


Is 


plot  (to  the  term  5  p).  The  first  four  lines  of  the  principal  series  are 
indicated  by  arrows  terminating  at  the  convergence  frequency  1  s,  the 
electron  falling  from  2  p,  3  p,  4  p,  5  p  respectively  to  1  s.  The  first  lines 
of  the  1st  and  2d  subordinate  series  are  indicated  by  arrows  terminating 
at  the  convergence  frequency  of  these  two  series,  etc. 


54 


ORIGIN  OF  SPECTRA 

90U9IBA   OMJ,  <° 


CO           II     -' 

-    1  ' 

Ni" 

o£ 

o           — 

^ 

^^ 

s 

II 

» 

c?"  3 

o  [0            tO  c\J 

1 

cog         r 

^     u,  * 

CO 

ID 

5r<          r- 

\  5 

s 

^' 

£  h         ^* 

•22         w 

^J 

5    o 

IS        Q) 

<* 

'c  ^ 

O                                            CO 

B 

10 

f    

.§<* 

o 

ID 

O    j^ 

^     ^ 

J 

N 

^D                                    ^MlO 

^  ro     ^-, 

Q 
to 

^ 

X. 

" 

1 



r-« 

o 

<M 

dT            ^H   „ 

9 

§ 

™ 

* 

CO 

00 

to 

to 

CO 

1 

I 

j 

1 

8 

tf       J 

H 


o 

P? 


d  £ 
o  -j 


ENERGY  DIAGRAMS  55 

Figure  6  shows  a  similar  diagram  for  the  arc  spectrum  of  magnesium, 
with  several  of  the  fundamental  lines  indicated  by  arrows.  Making 
use  of  the  quantum  relation  hc*v  =  eV  •  108,  we  may  express  wave  number 
in  terms  of  the  potential  difference  V  through  which  an  electron  must 
freely  fall  in  order  to  accumulate  an  amount  of  kinetic  energy  equivalent 
to  a  quantum  of  radiation  of  wave  number  v.  Expressed  in  volts  we  / 
find: 

Volts  =  V  =  1.2345  v  •  1(T4  )  ,.ON 

or  v   =81007  T 

Expressed  in  terms  of  wave-length  X  measured  in  Angstrom  units,  we 
find: 

V  =  12345/X.  (64) 

The  terminology  "volts"  by  universal  custom  is  used  to  signify  a 
variety  of  meanings  where  the  more  precise  statement  of  fact  requires 
several  words  and  is  inconvenient.  For  example,  instead  of  stating 
precisely  that  we  refer  to  the  velocity  of  an  electron  which  has  been 
accelerated  through  a  potential  difference  of  x  volts,  we  may  express 
this  fact  by  stating  that  the  electron  has  a  velocity  of  x  volts.  Similarly, 
we  may  use  the  expression  "an  energy  of  x  volts"  meaning  the  value  of 
the  kinetic  energy  of  the  electron  referred  to  above.  With  the  quantum 
relation  hc2v  —  eV-108  tacitly  understood,  we  may  speak  of  frequencies, 
wave  numbers  and  wave-lengths  of  x  volts,  meaning  for  example  the 
wave  number  derived  by  substituting  x  for  V  in  Equation  (63) ,  etc.1 

In  Figure  6,  for  example,  a  displacement  of  one  electron  to  the  left 
from  1  S  to  2  p2  requires  2.70  volts  work.  The  electron  in  returning  to 
1  S  gives  up  this  energy  as  a  quantum  of  radiation  of  wave-length  4573  A. 
The  arrow-head  shows  the  direction  and  end  of  the  displacement  in  each 
case. 

Figure  7  is  a  schematic  representation  of  the  enhanced  lines  of 
magnesium.  It  is  noted  that  one  of  the  valence  electrons  is  absent, 
which  fact  greatly  alters  the  values  of  the  different  energy  or  wave 
number  levels.  The  first  pair  of  each  of  the  three  series.  Prin.,  1  @  — 
m  $,  1st  Sub.,  2  <P  -  m  S>,  and  2d  Sub.,  2  $  -  m  @,  is  indicated  by 
arrows. 

The  above  examples  illustrate  the  usefulness  of  such  energy  diagrams. 
All  mathematically  possible  series  and  combination  lines  are  given  by 
the  frequency  differences  of  pairs  of  energy  levels.  The  various  levels, 

i  Language  serves  two  purposes;  one  in  a  definitional  sense,  where  preciseness  is  requisite; 
the  other  for  the  conveyance  of  ideas,  where  conciseness  is  essential.  It  is  in  the  latter  sense 
that  the  above  inexact  yet  unambiguous  notation  is  justifiable. 


56 


OF  SPECTRA 


4- 

1 

!- 

^            suoiioeig  £            ;^ 

• 

1 

u> 

. 

m 

suoj-^oai  g 

•  8 

a 

^      '8 

in 

6 

8 

.3 

— 

*~ 

m 

CD 

-2 

eo 

CX 

^~~ 

n 

od 

2 

i 

^ 

CO 

115     1 

3 

g 

1 

s 

UOJP913    33U9IBA  I 

S  tf    2 

U    -8 

J 

(8 

CO  CO 
0^  ^D 

^"*  CO 

«     a 
o   2     ^ 

"T 

~~~~~ 

«o   D     ^ 

<4 

J 

%9 

t-) 

SVN  1 

} 

j 

a 

B 

OJ 

\  1- 

<^    m      <u 

3|  - 

§      |    I                               ?5       SS    __ 

^  ^ 

OD   ^       £2 

-*-*            1 
05      i>    < 

"S      5^ 

«        ^   T 

-1      5  1 

J                                                     C" 

M        CKNI 

4.7  4 

Loo 

•epresentatio 

r     s 

.«    03                   p|^ 

CO                  o 

S  c           rt 

"* 

'Sco 

g 

^o 



S 

«?  £»'           ^ 

1> 

"* 

•^                  C5 



E- 



10 

. 

, 

1 

ENERGY  DIAGRAMS 


57 


CM 


2 
I 


a 


cd 


58 


ORIGIN  OF  SPECTRA 


ENERGY  DIAGRAMS  59 

however,  are  concerned  with  only  the  total  quantum  number.  No 
differentiation  between  azimuthal  and  radial  quantum  numbers  is 
made.  The  so-called  Grotrian  diagrams  remedy  this  difficulty.  These 
possess  the  additional  advantage  that  the  fine  structure,  doublets,  etc., 
may  be  readily  indicated. 

Figure  8  is  such  a  diagram  for  hydrogen.  Three  coordinates  are 
employed:  as  abscissa,  logarithm  of  the  wave  number;  as  ordinate,  the 
azimuthal  quantum  number;  and  a  third  system,  indicated  by  dotted 
lines,  the  sum  of  the  azimuthal  and  radial  quantum  numbers.  Each 
point  shown  by  a  small  circle  represents  a  wave  number  or  equivalent 
energy  level  which  may  be  computed  from  Equation  (20)  by  the  proper 
assignment  of  azimuthal  and  radial  quantum  numbers.  A  spectral 
frequency  is  indicated  by  a  straight  line  between  two  points  and  its 
numerical  value  is  given  by  the  difference  in  the  wave  numbers  corre^ 
spending  to  each  end  of  this  line.  By  the  Bohr  principle  of  selection  the 
change  in  azimuthal  quantum  number  =  ±  1.  Hence  all  straight  lines 
representing  spectral  frequencies  must  terminate  in  adjacent  horizontal 
lines  of  constant  azimuthal  quantum  number.  The  group  terminating 
at  the  upper  right-hand  point  represents  the  Lyman  series,  each  member 
-of  which  is  a  singlet.  The  plot  shows  Ha  and  H^  of  the  Banner  series, 
each  member  being  a  triplet  and  hence  appearing  three  times.  The 
first  line  of  the  Paschen  series,  which  is  a  quintuplet,  appears  five  times 
on  the  chart,  and  is  designated  by  the  letter  P. 

In  a  similar  manner  the  spectra  of  the  heavier  elements  may  be 
illustrated.  Figure  9  represents  sodium.  The  double  mp  terms,  all 
having  the  same  azimuthal  quantum  number  2,  are  shown  by  mpi  and 
mp2.  All  lines  representing  the  principal  series  terminate  at  the  upper 
right-hand  point  and  each  occurs  twice  on  account  of  the  double-p 
values.  The  two  D-lines  are  marked  with  their  proper  wave-lengths. 
The  straight  lines  representing  the  1st  and  2d  subordinate  series  all 
terminate  at  2  p  and  again  occur  twice  because  of  the  double  values  of 
mp.  The  above  discussion  illustrates  the  use  and  construction  of  these 
diagrams  for  representing  series  relations.  We  shall  have  occasion  to 
refer  to  them  subsequently. 


Chapter  III 
lonization  and  Resonance  Potentials  for  the  Elements 

When  electrons  are  accelerated  through  gas  or  vapors  there  are, 
especially  for  monatomic  gases  having  a  small  electron  affinity  and  the 
metallic  vapors,  well-defined  critical  velocities  at  which  a  large  transfer 
of  energy  takes  place  between  electrons  and  atoms.  For  velocities 
below  this  minimum  critical  value  the  collision  is  elastic,  the  electron 
rebounding  from  the  atom  with  usually  an  alteration  in  its  direction 
of  path  but  with  the  same  kinetic  energy.  In  general  two  types  of 
inelastic  collision  occur,  one  in  which  an  outer  electron  of  the  atom 
undergoes  an  interorbital  transition,  and  the  other  in  which  an  outer 
electron  is  completely  removed.  In  the  latter  case  the  atom  is  "  simply" 
ionized,  having  a  total  net  charge  +  e>  The  potential  through  which  an 
electron  must  fall  in  order  to  accumulate  just  sufficient  velocity  to 
produce  the  first  type  of  inelastic  collision  has  been  termed  by  Tate  and 
Foote  the  resonance  potential.  The  corresponding  value  for  a  collision 
resulting  in  ionization  is  known  as  the  ionization  potential.  In  general 
there  may  be  several  ionization  potentials  corresponding  to  the  removal 
of  1,  2,  3,  etc.  electrons,  but  only  simple  ionization  will  be  considered  in 
the  present  section.  Experimental  evidence  has  shown  that  the  loss 
in  kinetic  energy  of  the  impacting  electron  during  a  collision  of  the 
"  resonance"  type  is  equal  to  the  resonance  potential, '  whether  the 
initial  energy  be  exactly  equal  to  or  greater  than  that  corresponding 
to  the  resonance  potential.  Whether  or  not  this  be  true  in  the  case  of 
ionization  remains  to  be  demonstrated,  for  it  is  possible  that  the  ejected 
electron  may  leave  the  atom  with  any  velocity  whatever,  depending 
upon  the  nature  of  the  impact. 

Since  energy  is  abstracted  from  the  impacting  electron  and  absorbed 
by  the  atom,  the  total  energy  of  the  atom,  following  a  collision,  is  in- 
creased by  an  amount  equivalent  to  either  the  resonance  or  ionization 
potential.  When  the  atom  subsequently  returns  to  its  normal  state  this 
energy  is  emitted  in  the  form  of  radiation.  In  the  case  of  ionization  the 
electron  may  return  by  a  variety  of  interorbital  transitions,  each  resulting 

60 


IONIZATION  AND  RESONANCE  POTENTIALS          61 

in  an  emission  of  a  quantum  of  wave  number  vk)  subject  to  the  conserva- 

fon  of  energy  condition: 


energy  condition: 

eVt  -  108, 


where  Vt  is  the  ionization  potential.     With  numerous  atoms  and  elec- 
trons returning  to  equilibrium  in  different  manners,  we  have  as  the 
composite  result  an  emission  of  the  complete  arc  spectrum.     If  an  elec- 
tron returns  to  the  normal  orbit  directly  without  passing  through  inter- 
:  mediate  states  of  equilibrium,  but  one  frequency  is  emitted,  which  is 
j  the  highest  frequency  in  the  arc  spectrum.     This  frequency,  as  is  evident 
]  from  a  consideration  of  the  energy  diagrams  Figures  4  to  9  and  Equations 
I  (34)  to  (37),  is  the  highest  convergence  frequency  of  any  series  of  the 
I  arc  spectrum,  the  wave  numbers  1  s  for  the  alkalis  and  1  S  for  the  metals 
of  Group  II. of  the  periodic  table.     In  the  normal  unexcited  atom,  ac-   \ 
cordingly,  the  outer  electron  concerned  with  emission  of  spectral  lines  lies  J 
in  the  1  s  or  1  S  orbit. 

The  energy  absorbed  by  the  atom  at  the  resonance  potential  is  not 
great  enough  to  completely  eject  an  electron,  but  rather  is  just  sufficient 
to  displace  it  to  a  neighboring  orbit  of  higher  energy  value.  We  havev 
found  experimentally  that  the  alkali  metals  possess  a  resonance  potential } 
corresponding  exactly  to  the  amount  of  work  required  to  displace  an/ 
electron  from  the  1  s  orbit  to  the  2  p  orbit,  the  first  energy  level  above^ 
1  s.  For  sodium,  as  illustrated  by  Figure  5,  the  energy  absorbed  by 
the  atom  is  2.10  volts.  The  electron  accordingly  in  returning  to  its 
normal  orbit  releases  this  amount  of  energy  as  a  quantum  of  radiation, 
of  wave  number  v  =  1 .  s  —  2  p;  that  is,  the  D-lines  and  no  other  lines 
of  the  sodium  spectrum  are  emitted.  Since  both  D-lines  are  emitted 
it  may  be  expected  that  two  resonance  potentials  exist,  but  if  so  the 
difference  in  their  values  would  be  many  times  less  than  our  errors  of 
measurement.  It  is  doubtful  whether  any  conclusion  in  this  regard  may 
be  drawn  from  the  fact  that  we  found  a  single  resonance  potential  for 
caesium  where  the  doublet  separation  is  considerably  larger.  There  is 
on  the  other  hand  a  vague  possibility  that  the  component  of  higher 
frequency  is  the  determining  factor  for  the  resonance  potential,  in 
rather  superficial  analogy  to  the  excitation  of  the  K  series  at  the  mini- 
mum potential  corresponding  to  Ka. 

In  the  case  of  the  metals  of  Group  II  of  the  periodic  table  the  authors 
have  found  that  two  resonance  potentials  exist.  One  of  these  cor- 
responds to  the  energy  required  to  displace  an  electron  from  its  normal 
position  in  the  1  S  orbit  to  the  neighboring  orbit  2  p2.  The  electron  in 


62 


ORIGIN  OF  SPECTRA 


returning  to  the  1  S  orbit  gives  up  this  energy  as  a  quantum  of  radiation 
of  wave  number  v  =  1  S  —  2  p2.  Only  the  single  line  is  emitted.  In 
fact  the  corresponding  frequencies  IS  —  2pi  and  IS  —  2  p3  are  absent 
even  in  the  complete  arc  spectra  of  these  metals.  The  reason  for  these 
missing  terms  is  explained,  not  at  all  satisfactorily ,  however,  by  Sommer- 
feld's  theory  of  "  internal  quantum  numbers"  and  is  beyond  the  scope  of 
the  present  book.1 

TABLE  X 
RESONANCE  AND  IONIZATION  POTENTIALS,  GROUP  I 


Element 

z 

Series 
Notation 

V 

Volts 

Computed 

Observed 

Li  

3 
11 
19 
29 
37 
47 
55 
79 

Is 
ls-2Pl 

Is 
ls-2Pl 

Is 
ls-2Pl 

Is 

Is  -  2  Pl 

Is 
1  s  -  2  pi 

Is 
la-2p, 

Is 
1  s  -  2  pi 

Is 
ls-2pl 

43,486 
14,903 

41,449 
16,973 

35,006 
13,043 

62,308 
30,784 

33,689 
12,817 

61,096 
30,473 

31,405 
11,732 

70,000? 
41,174 

5.368 
1.840 

5.116 
2.095 

4.321 
1.610 

7.692 
3.800 

4.158 
1.582 

7.542 
3.762 

3.877 
1.448 

8  to  9? 
5.1 

5.13 
2.12 

4.1 
1.55 

4.1 
1.6 

3.9 
1.48 

Na  ..  ... 

K 

Cu 

Rb      .    . 

Ag.. 

Cs  
Au  

The  second  resonance  potential  corresponds  to  the  energy  required 
to  displace  an  electron  from  its  normal  position  in  the  1  S  orbit  to  the  2  P 
orbit.  If  the  electron  returns  directly  to  the  1  S  orbit  without  passing 


Sommerfeld,  "  Atombau,"  3d  Ed.,  Chap.  6,  Section  5. 


IONIZATION  AND  RESONANCE  POTENTIALS         63 

through  intermediate  states  of  equilibrium,  this  energy  is  liberated  as  a 
i  quantum  of  radiation  of  wave  number  v  =  1  S  —  2  P.    These  transi- 
tions are  illustrated  in  the  case  of  magnesium  by  Figure  6,  the  resonance 
potentials  being  2.70  and  4.33  volts. 

In  general  we  note  that  the  ionization  potential  of  a  monatomic 
vapor  corresponds  to  the  highest  convergence  frequency  in  the  arc 
spectrum  of  the  material;  to  the  limit  of  a  series  the  first  line  of  which 
corresponds  to  a  resonance  potential.  Exceptions  to  this  general  rule 
will  be  given  individual  attention  later.  As  will  be  considered  in  more 
detail  under  a  separate  section2  these  series  are  absorption  lines  for  the 
normal  atom,  so  that  ionization  and  resonance  potentials  in  certain 
cases  may  be  predicted  from  a  knowledge  of  the  prominent  absorption 
lines. 

Group  I:  Table  X  shows  the  ionization  and  resonance  potentials 
for  metals  in  Group  I  of  the  periodic  table.  The  computed  values  are 
obtained  from  the  series  relationships  and  are  to  be  preferred  to  our 
direct  experimental  values  for  all  computations  in  which  a  consideration 
of  ionization  and  resonance  potentials  enters.  No  satisfactory  results 
have  been  obtained  with  copper,  silver  and  gold,  although  we  have  made 
very  elaborate  and  extensive  experiments.  The  difficulty  is  of  a  pyro- 
metric  nature,  temperatures  of  2000°  C  and  a  high  vacuum  being  re- 
quired. However,  from  series  relationships  and  a  consideration  of  the 
absorption  or  "  reversed"  lines  the  computed  values  are  probably  correct. 

Group  II:  Table  XI  shows  the  computed  values  of  the  resonance 
and  ionization  potentials  for  elements  of  Group  II  of  the  periodic  table, 
together  with  the  experimental  values  obtained  by  the  authors.3 

Group  III:  The  series  relations  in  this  group,  which  includes  alumi- 
num, gallium,  indium,  and4  thallium,  should  be  similar  to  that  of  the 
alkali  metals.  The  arc  lines  have  been  beautifully  correlated  in  series  of 
this  type,  consisting  of  widely  spaced  doublets,  but  the  convergence 
frequency  of  the  principal  series  is  smaller  than  that  of  the  subordinate 
series  —  a  fact  not  easily  reconciled  with  the  quantum  theory  unless 
the  observed  principal  series  is  of  a  second  type  converging  at  2  s  instead 
of  1  s.  This  would  indicate  that  the  most  important  principal  series 
which  converges  at  1  s  is  as  yet  undiscovered.  If  so  most  of  the  lines 
except  the  first  term  should  lie  in  the  extreme  ultra-violet.  It  is  of 
interest  that  several  lines  supposedly  of  the  arc  spectrum  have  been 
observed  which  have  a  greater  wave  number  than  the  highest  known 

a  Cf.  Chapter  IV. 

8  For  data  by  other  observers,  see  general  references  at  end  of  chapter.  Several  of  the. 
experimental  values  in  Tables  X  and  XI  were  obtained  by  Tate  and  Foote. 


64 


ORIGIN  OF  SPECTRA 


convergence  frequency,    again  indicating  that  1  s  remains   to  be  dis- 
covered.4 

TABLE  XI 
RESONANCE  AND  IONIZATION  POTENTIALS,  GROUP  II 


Element 

Z 

Series 

V 

Vc 

>lts 

Notation 

Computed 

Observed 

Be 

4 

>  Mg  ? 

>  Mg? 

Mg 

12 

IS 

61,672 

7.613 

7.75 

Ca  

20 

!S-2p2 
IS-2P 

IS 

21,871 
35,051 

49,305 

2.700 
4.327 

6.087 

2.65 
4.42 

6.01 

Zn  

30 

!S-2p2 
1S-2P 

IS 

15,210 
23,652 

75,767 

1.878 
2.920 

9.353 

1.90 

2.85 

9.3 

Sr  

38 

lS-2p2 
1S-2P 

IS 

32,502 
46,745 

45,926 

4.012 
5.771 

5.670 

4.18 
5.65 

Cd  

48 

lS-2p2 
1S-2P 

IS 

14,504 
21,698 

72,539 

1.791 
2.679 

8.955 

8.92 

Ba  

56 

!S-2p2 
1S-2P 

IS 

30,656 
43,692 

42,029 

3.784 
5.394 

5.188 

3.95 
5.35 

Hg.  . 

80 

lS-2p2 
1S-2P 

IS 

12,637 
18,060 

84,178 

1.560 
2.230 

10.392 

10.2 

Ra  

88 

!S-2p2 
1S-2P 

IS 

39,413 
54,066 

40-50000? 

4.866 
6.674 

5-5.5? 

4.76 
6.45 

!S-2p2 
IS-2P 

12,500? 
20,700? 

1.5? 
2.6? 

4  These  are  conveniently  summarized  in  tables  by  Fowler,  "  Report  on  Series  in  Line 
Spectra,"  Chap.  17. 


ION  I Z AT  ION  AND  RESONANCE  POTENTIALS         65 

The  only  critical  potentials  known  for  this  family  are  our  measure- 
ments on  thallium,  which  are  rather  unsatisfactory.  We  found  a  reso- 
nance potential  1.07  volts  and  an  ionization  potential  7.3  volts.  The 
resonance  potential  corresponds  closely  to  the  component  of  higher 
frequency  of  the  first  pair  of  Paschen's  principal  series  usually  given  as 
P  =  1  s  —  3  pi  but  which  more  likely  should  have  the  notation  v  —  2  s 
—  3  pi  =  8683.3  o  1.07  volts.  This  exact  agreement  with  experiment 
is  accidental,  and  in  case  this  frequency  is  2  s  —  3  pi,  it  probably  has  no 
physical  significance  whatever,  as  the  determining  wave  number  then 
should  be  1  s  —  2  pi.  The  observed  ionization  potential  corresponds 
to  a  value  of  1  s  of  about  the  magnitude  to  be  expected  but  greater  than 

|  any  convergence  frequency  known  at  present.  More  observations  on 
critical  potentials  for  this  group  should  be  made;  our  work  on  thallium 
should  be  repeated  with  greater  care;  and  the  spectral  series  relations 
should  be  further  investigated  with  the  object  of  finding  higher  con- 
vergence frequencies  for  the  principal  series  of  all  the  metals  of  this 
family. 

Group  IV:  The  series  relations  for  this  family  are  in  a  very  un- 
satisfactory state,5  and  there  is  little  hope  for  directly  determining  the 

j  critical  potentials  of  such  highly  refractory  elements,  except  lead,  unless 
an  entirely  new  method  of  experimentation  should  be  devised.  We  have 
tried  without  success  the  vaporization  of  such  refractory  materials  in  a 
high  vacuum,  using  a  small  crucible  and  projecting  an  approximately 

j  unidirectional  stream  of  the  vapor  through  the  ionization  chamber. 

i  The  problem  is  most  difficult  both  from  the  standpoint  of  electrical 

:   measurements  and  of  pyrometry.     Our  results  with  lead  by  the  usual 

'  method  gave  for  the  resonance  potential  1.26  volts  and  for  the  ionization 
potential  7.93  volts.  The  first  point  coincides  with  an  isolated  group  of 
infra-red  lines,  observed  by  Randall,  the  shortest  wave-length  of  which 

•  is  X  =  10291  =0=  1.30  volts. 

Group  V:  Series  relations  are  unknown6  and  it  is  questionable 
whether  measurements  on  critical  potentials  of  polyatomic  vapors 
give  any  direct  indication  of  spectral  frequencies  of  line  series  since 

,  the  work  of  ionization,  for  example,  may  include  that  of  dissociation 
of  the  molecule  into  atoms.7  It  is  even  possible  that  the  band  spectra 
of  polyatomic  vapors  are  more  closely  related  to  the  values  indicated 
by  critical  potentials.  In  Table  XII  the  potentials  for  antimony  and 

*  Fowler  summarizes  the  present  meager  knowledge  of  the  series  spectra  of  these  elements 
in  two  pages,  loc.  cit.,  pp.  163^. 

•  Fowler,  loc.  cit.,  p.  164. 

i  See  latter  part  of  Chap.  VIII. 


66 


ORIGIN  OF  SPECTRA 


bismuth  are  unreliable.  Although  we  have  made  numerous  deter- 
minations each  one  of  which  appeared  satisfactory  by  itself,  the  different 
observations  showed  wide  deviations,  possibly  accounted  for  by  the 
formation  of  polarization  films  on  the  electrodes.  It  should  be  pointed 
out  that  observations  on  ionization  potentials  without  corresponding 
data  on  resonance,  for  velocity  corrections,  are  of  little  value  with  non- 
metallic  vapors,  as  surprisingly  large  errors  arise  in  "  initial  velocities" 
determined  by  the  usual  velocity  distribution  curves.  Such  is  not  the 
case  with  metallic  vapors  and  the  rare  gases. 


TABLE  XII 
RESONANCE  AND  IONIZATION  POTENTIALS,  GROUP  V 


Element 

Z 

Observed  Potential, 
Volts 

Remarks 

Resonance 

Ionization 

N              

7 

15 
33 
51 
83 

8.18 

5.80 
4.7 
? 
2.0 

16.9 

13.3 
11.5 

7.8-8.5 
8.0-8.5 

Lines  at  X  1494.8  and 
\1492.8o  8.27  volts. 
Ionization  at  17.75, 
25.4,  30.7  observed 
by  Brandt.8 

Uncorrected  for  initial 
velocity. 

P....  

As  

Sb 

Bi     

Group  VI:  Our  knowledge  of  the  spectral  series  of  these  elements 9 
is  confined  to  oxygen,  sulphur  and  selenium.  Principal,  1st  and  2d 
subordinate  series  of  both  single  lines  and  triplets  are  known  for  oxygen, 
and  a  similar  triplet  structure  for  sulphur  and  selenium.  There  is  no 
apparent  relation  between  the  values  of  the  series  terms  and  the  observed 
critical  potentials.  For  example,  Fowler  lists  1  S  and  1  s  for  oxygen 
as  v  —  33043  and  v  —  36069  respectively,  corresponding  to  roughly 
four  volts,  whereas  the  ionization  potential  is  nearly  sixteen  volts.  This 


•Brandt,  Z.  Physik,  8,  pp.  32-44  (1921). 
Hughes,  general  references  at  end  of  chapter. 
» Fowler,  loc.  cit.,  p.  166. 


For  data  on  nitrogen  by  other  observers  see 


IONIZATION  AND  RESONANCE  POTENTIALS 


67 


lack  of  agreement  might  be  due  to  the  fact  that  the  wave  number  v  — 
33043  is  really  2  S  instead  of  1  S  and  that  1  S  is  as  yet  unknown.-  On 
the  other  hand  it  is  more  probable  that  the  ionization  potential  is  char- 
acteristic of  the  molecule,  as  above  mentioned,  and  hence  has  only  a 
remote  relation  to  spectral  frequencies  for  the  atom.  Table  XIII 
summarizes  our  data  on  several  of  the  polyatomic  elements  in  this 
group.  The  values  for  selenium  and  for  tellurium  are  questionable. 

TABLE  XIII 
RESONANCE  AND  IONIZATION  POTENTIALS,  GROUP  VI 


Element 

Z 

Observed  Potential 
Volts 

Remarks 

Resonance 

Ionization 

o 

8 
16 
34 
52 

7.91 
4.78 
3.0-3.5 
2.3-2.9 

15.5 
12.2 
12-13 
? 

See  Hughes  10  for  data 
by  other  observers. 

(12.7  observed  by 
Udden.)" 

s  

Se  

Te 

Group  VII:  Spectral  relations  unknown.12  Hughes  and  Dixon13 
observed  a  critical  potential  in  chlorine  at  8.2  volts  and  in  bromine  at 
10.0  volts,  but  whether  these  are  ionization  or  resonance  potentials  is 
uncertain.  For  iodine  we  have  found  a  resonance  potential  of  2.34  ± 
0.2  volts  and  an  ionization  potential  of  10.1  ±  0.5  volts.  Smyth  and 
Compton14  observed  ionization  of  molecule  at  9.4  volts,  ionization  of 
atom  at  8.0  volts  and  ionization  of  fluorescing  molecule  at  6.8  volts. 

Saha,  Nature,  107,  p.  683  (1921),  states  that  Catalan  in  some  unpub- 
lished work  has  found  1  S  for  manganese.  His  value  gives  7.38  volts^ 
for  the  computed  ionization  potential,  which  is  consistent  with  the 
behavior  of  the  element  in  the  solar  spectrum,  as  mentioned  on  page  172. 

Groups  VIII  &  0:  Table  XIV  summarizes  mainly  the  work  of  Horton 
and  Davies15  on  the  rare  gases,  work  which  has  been  done  apparently 

10  See  general  references  at  end  of  chapter. 

"Udden,  Phys.  R.,  18,  p.  385  (1921). 

12  Fowler,  loc.  cit.,  p.  173,  summarizes  some  data  on  manganese  triplets. 

"  Hughes  and  Dixon,  Phys.  R.,  10,  p.  495  (1917). 

14  Smyth  and  Compton,  Phys.  R.,  16,  pp.  501-13  (1920). 

15  Horton  and  Davies,  Proc.  Roy.  Soc.,  95,  p.  408  (1919);  97,  p.  1   (1920);    98,  p.  121 
(1920);    Phil.  Mag.,  39,  p.  592  (1920). 


68 


ORIGIN  OF  SPECTRA 


with  high  precision  and  the  greatest   experimental    skill.     The  data 
of  these  and  other  observers  are  tabulated  by  Hughes. 

TABLE  XIV 
RESONANCE  AND  IONIZATION  POTENTIALS,  GROUP  0 


Element 

Z 

Observed  Potential  Volts 

Resonance 

lonization 

He  

2 

10 

18 

20.4 
21.2 

11.8 

17.8 

11.5    . 

25.6 
(25.4 

(25.5 

16.7 
20.0 

22.8 

15.1 

Franck  and  Knipping16 
later  25.3) 
Compton  17) 

Ne  

A  

No  data  on  the  metals  exist  either  in  regard  to  spectral  series18 
or  critical  potentials. 

Hydrogen.  Hughes  lists  the  work  of  eleven  groups  of  experimenters. 
In  Table  XV  we  summarize  the  values  obtained  by  Horton  and  Davies19 
and  by  ourselves.20 

TABLE  XV 
RESONANCE  AND  IONIZATION  POTENTIALS,  HYDROGEN 


Resonance 

lonization 

Observers 

1st 

2d 

1st 

2d 

10.5 

13.9 

14.4 

16.9 

Horton  and  Davies 

10.4 

12.0 

13.3 

16.0 

Mohler  and  Foote  (Revised 

from  more  recent  data. 

Earlier  published  values 

were  12.2  and  16.5) 

"  Franck  and  Knipping,  Zeit.  Physik,  1,  p.  320  (1920). 

"  Compton,  Phil.  Mag.,  40,  p.  553  (1920). 

18  Constant  difference  groups  are  known,  suggesting  that  series  relations  exist. 

19Proc.  Roy.  Soc.,  97,  p.  23,  1920. 

20  Mohler  and  Foote,  Bur.  Standard  Sci.  Paper,  400;  Phys.  R.,  19,  pp.  419-20  (1922). 


ION  I  Z  AT  ION  AND  RESONANCE  POTENTIALS          69 

THE  NORMAL  HELIUM  ATOM 

While  the  quantum  theory  yields  results  of  the  greatest  precision  in 
the  case  of  ionized  helium,  a  satisfactory  interpretation  of  the  normal 
helium  atom  with  two  electrons  proves  to  be  very  difficult.  The  simple 
Bohr  theory  assumed  that  the  two  electrons  revolved  in  a  single  circular 
orbit  about  the  nucleus  of  charge  +  2  e.  By  Equation  (50)  we  obtain 
accordingly  for  the  total  energy  of  the  atom: 


W  =  -  2         (2  -  0.25)2  =  -  1.321  -  KT10  ergs  =c=  -  83.0  volts.     (65) 

The  energy  of  the  simply  ionized  atom  is  obtained  by  the  same  equation 
or  by  Equation  (20)  and  gives  directly  the  value  —  54.2  volts  concerning 
which  there  can  be  no  question,  as  it  is  derived  from  the  solution  of  the 
simple  problem  of  two  bodies  which  has  been  amply  developed  and 
verified  in  the  earlier  part  of  this  book.  The  difference  in  these  two 
values,  83.0  —  54.2  =  28.8  volts,  should  give  the  ionization  potential 
of  helium,  whereas  by  direct  experiment  we  find  about  25.5  volts,  a 
sufficiently  unsatisfactory  agreement  to  warrant  the  rejection  of  this 
structure  for  the  normal  helium  atom.  Furthermore  it  is  not  in  accord 
with  the  known  diamagnetic  properties  of  helium. 

Helium21  possesses  two  independent  groups  of  series  in  its  arc  spec- 
trum, a  single  line  and  a  doublet  system,  between  which  no  combinations 
whatever  occur.  This  peculiar  behavior  immediately  suggests  that  the 
systems  arise  in  two  entirely  different  configurations  of  the  helium  atom. 
In  fact  it  was  once  thought  that  helium  must  be  a  mixture  of  two  gases, 
for  convenience  called  orthohelium  and  parhelium,  names  now  retained 
to  denote  the  two  types  of  atomic  configuration. 

Figure  10  shows  the  series  relations  for  helium.  The  upper  half 
represents  the  single-line  system  ascribed  to  parhelium.  The  lower 
half  of  the  figure  shows  the  doublet  system  of  orthohelium.  The  doub- 
lets are  exceedingly  close  and  hence  do  not  appear  resolved  in  this  dia- 
gram. In  the  notation  we  represent,  as  usual,  singlet  series  by  capital 
letters  and  doublet  series  by  lower  case  letters.  The  highest  convergence 
limits  2  S  and  2  s  for  these  two  groups  correspond  respectively  to  3.954 
and  4.747  volts.  If  either  of  these  states  represented  the  normal  atom, 
one  of  the  values  named  should  be  the  ionization  potential,  and  the 
stability  of  the  atom  would  be  but  1/7  the  observed  stability.  The 
most  obvious  step  accordingly  is  to  identify  the  normal  state  with 
either  1  S  or  1  s,  to  which  should  correspond  the  experimental  value  for 
the  ionization  potential. 

21  Fowler,  loc.  cit.,  p.  89. 


70 


ORIGIN  OF  SPECTRA 


Nedotiv*  Enerdies  on  Wave  Number  S  101*  1 10      (TVrm  Values) 


FIG.  10.     The  series  relationships  for  helium.    (From  Kemble,  Phil.  Mag.  42,  p.  124; 

1921.) 


FIG.  11.     The  normal  helium  atom. 


ION  I Z  AT  ION  AND  RESONANCE  POTENTIALS          71 

1  he  first  electron  bound  to  the  helium  nucleus  revolves  in  a  1  quan- 
tum circular  orbit.  The  second  electron  cannot  in  the  normal  state 
revolve  in  a  coplanar  orbit  which  surrounds  the  first  because  (a)  the 
readily  computed  energy  relations  are  not  in  agreement  with  ionization 
potential  measurements  and  (b)  the  configuration  would  resemble 
lithium  and  should  have  a  positive  valence.  As  already  mentioned 
(cf.  discussion  of  Equation  (65)),  the  two  electrons  cannot  revolve  in 
the  same  orbit,  and  as  Bohr  points  out  there  is  no  type  of  transition  con- 
ceivable between  a  state^where  the  electrons  occupy  different  orbits  and 
that  state  in  which  the  same  orbit  is  occupied. 

Bohr22  concludes  that  in  the  normal  state  both  electrons  move  in 
1  quantum  paths  which  make  an  angle  of  120  degrees  with  each  other 
as  shown  in  Figure  11.  To  a  first  approximation  these  are  circular 
orbits.  On  account  of  the  mutual  action  of  the  two  electrons,  however, 
there  is  a  slight  deviation  from  the  true  circle,  and  the  two  orbits  rotate 
slowly  about  the  fixed  axis  of  angular  momentum  of  the  atom.  Bohr 
states  that  while  the  mathematical  analysis  of  this  three-body  problem 
is  not  yet  complete,  preliminary  computations  indicate  that  it  will  give 
the  correct  value  of  the  ionization  potential. 

Lande23  has  shown  that  the  single-line  system  belongs  to  a  crossed- 
orbit  configuration,  where  one  of  the  electrons  undergoes  interorbital 
transitions,  while  the  doublet  system  arises  in  transitions  of  the  outer 
electron  in  a  coplanar  configuration.  We  accordingly  assign  the  singlet 
spectra  to  parhelium  and  the  doublet  spectra  to  orthohelium.  Normal 
helium  is  therefore  the  1  S  state  of  parhelium.  In  the  2  s  state  of  ortho- 
helium  the  inner  electron  revolves  in  a  1  quantum  circular  orbit,  while 
the  outer  electron,  according  to  Bohr,  moves  in  a  coplanar  elliptical 
orbit  of  total  quantum  number  2  and  azimuthal  quantum  number  1. 
The  1  s  state  should  therefore  require  two  electrons  in  the  same  circular 
orbit  at  opposite  ends  of  a  diameter.  Although  this  is  the  most  stable 
type  of  configuration,  Bohr,  as  stated  above,  concludes  it  cannot  be 
formed,  and  accordingly  we  have  no  term  1  s  in  the  helium  spectrum,  a 
hypothesis  also  advanced  by  Franck  and  Reiche24  from  other  consider- 
ations. 

Since  Bohr's  mathematical  computations  on  the  dynamics  of  these 
systems  have  not  been  published,  we  shall,  following  Franck  and  Knip- 
ping,25  compute  1  S  from  their  observation  on  the  ionization  potential. 

22  Bohr,  Z.  Physik,  9,  pp.  1-67  (1922). 

"Physik.  Z.,  20,  pp.  228-34  (1919);   21,  pp.  114-22  (1920). 

24  Z.  Physik,  1,  pp.  154-160  (1920). 

2'Z.  Physik,  1,  p.  320  (1920). 


72  ORIGIN  OF  SPECTRA 

One  obtains  1  S  —  202910  =0=  25.3  volts.  Using  the  spectroscopically 
determined  values  of  2  S  and  2  s,  as  shown  in  Figure  10,  we  find 

'1S-2S  =  202910  -  32031  =  170880  =c=  21.1  volts 
1  S  -  2  s  =  202910  -  38453  =  164460  o  20.6  volts 

These  potentials  correspond  to  the  resonance  potentials  of  helium, 
the  observed  values  of  which  are  21.2  and  20.4  volts,  as  given  in  Table 
XIV.  It  therefore  appears  that  a  21.1  volt  impact  ejects  an  electron 
from  the  normal  1  S  state  to  the  2  S  state  of  parhelium,  while  a  20.6  volt 
impact  ejects  an  electron  from  the  normal  1  S  state  of  the  crossed  orbit 
system  to  the  2  s  state  of  the  coplanar  system,  orthohelium. 

The  existence  of  the  wave  number  1  S  immediately  suggests  the 
presence  of  a  principal  series  of  the  form  1  S  —  wP.the  first  few  terms 
of  which  may  be  computed  from  the  known  values  of  mP  as  follows : 


Notation 

V 

X 

1  ,S 

-  2P 

175  730 

569  A 

1  S 

-3P  

190,810 

524 

1  fi 

-4P 

196  100 

510 

Spectroscopic  measurements  have  not  as  yet  shown  the  presence  of  this 
series.  Fricke  and  Lyman26  observed  only  the  single  line  at  X  585.  This 
apparently  has  the  notation  1  S  —  2  S,  for  the  computed  value,  cor- 
responding to  the  resonance  potential  21.1  volts,  is  exactly  this  wave- 
length. The  excitation  of  1  S—  2  Sis  contrary  to  the  Bohr  principle  of 
selection,  but  the  line  was  emitted  in  a  strong  spark  where,  on  account 
of  the  presence  of  the  electrostatic  field,  the  selection  principle  is  not 
applicable.  The  line  would  not  be  absorbed  by  the  surrounding  un- 
excited  gas,  as  for  this  the  selection  principle  would  hold.  Lines  of  the 
series  1  S  —  mP,  on  the  other  hand,  should  show  very  great  absorption. 
This  probably  explains  why  Fricke  and  Lyman  could  detect  in  their 
experiments  the  emission  of  only  the  line  1  S  —  2  S.  If  one  could  devise 
a  continuous  source  of  ultra-violet  radiation  in  this  extreme  spectral 
range,  it  might  be  possible  to  obtain  the  series  1  S  —  mP  as  absorption 
lines,  analogous  to  Wood's  work  with  sodium,  page  80.  Possibly 
"exploded  wires"27  could  be  employed  to  advantage  in  this  respect. 

2«  Phil.  Mag.,  41,  p.  814  (1921).     See  footnote  39,  page  77. 
27  Anderson,  Astrophys.  J.,  51,  pp.  37-48  (1920). 


ION  I Z  AT  ION  AND  RESONANCE  POTENTIALS 


73 


Using  the  photo-electric  method  described  on  page  137  Franck  and 
Knipping28  have  obtained  in  helium  at  very  low  pressure  some  evidence 
for  the  presence  of  the  lines  1  S  —  2  P  and  1  S  —  3  P.  Their  results 
expressed  in  volts  are  as  follows: 


Notation 

Volts  computed 

Volts  observed 

1  fi 

-2P                

21.85 

21.9 

1  S 

-  3P                                   . 

23.7 

23.6 

The  method  is  not  conclusive,  but  merely  suggestive. 

If  electrons  are  ejected  to  the  2  s  or  2  S  orbits  of  trie  helium  atoms 
by  low  voltage  electronic  bombardment,  it  would  appear  that  they 
should  have  difficulty  in  returning  to  the  normal  state.  The  return 
to  1  S  from  2  s  is  prevented  by  the  general  law  that  intercornbination 
lines  between  the  crossed  and  coplanar  orbital  systems  do  not  take  place. 
The  return  from  2  S  is  contrary  to  the  selection  principle  and  should 
therefore  require  the  presence  of  a  disturbing  field.  Hence  the  2  s  and 
2  S  states  should  represent  metastable  forms  of  helium,  at  least  capable  of 
existing  for  an  appreciable  length  of  time  which  is  much  greater  than 
the  life  of  the  2  P  state,  for  example.29  This  is  evidenced  by  experi- 
mental work  on  the  absorption  of  helium  excited  by  a  mild  electric 
discharge.  Paschen30  observed  that  the  gas  very  readily  absorbed 
the  lines  2  S  -  2  P,  X  =  20582  and  2  s  -  2  p,  X  =  10830.  These  lines 
were  also  reemitted  as  resonance  radiation  (see  page  86).  From  the 
fact  that  the  scattered  or  resonance  radiation  for  2  s  —  2  p  was  probably 
greater  than  that  for  2  S  —  2  P,  Franck  and  Reiche  concluded  that 
only  the  state  2  s  should  be  considered  as  a  metastable  modification  of 
helium.  In  the  2  s  state  with  one  electron  revolving  about  the  other  in  a 

28  Loc.  cit. 

29  Since  the  above  was  written  a  paper  more  directly  bearing  on  this  point  has  been 
published  by  Kannenstine,  Astrophys.  J.,  55,  p.  345  (1922).    A  two-electrode  Wehnelt  arc  in 
helium  was  excited  by  an  alternating  potential  and  the  current- voltage  characteristics  were 
observed  by  use  of  a  Braun-tube  oscillograph.    Operations  were  so  controlled  that  after  the 
arc  had  struck  at  a  potential  above  the  normal  ionization  point,  it  could  be  maintained  at 
voltages  as  low  as  4.8  volts.    This  voltage  corresponds  to  the  wave  number  2s  and  accord- 
ingly represents  the  ionization  potential  of  the  helium  atom  in  its  2s  state.    Now  with  a  60 
cycle,  applied  potential,  the  arc  was  extinguished  with  each  cycle,  and  was  struck  again  only 
when  the  potential  was  greater  than  25  volts.    However,  when  the  frequency  of  the  applied 
potential  was  increased  to  between  200  and  220  cycles,  the  arc  both  struck  and  broke  at  4.8 
volts.    This  is  interpreted  to  mean  that  the  average  life  of  the  metastable  helium  atom  in 
the  2s  state  is  about  one-half  of  the  cycle,  or  of  the  order  0.002  seconds.    As  will  appear  in 
the  section  on  "The  Measurement  of  T,"  Chap.  IV,  the  time  during  which  an  outer  orbit, 
not  constituting  a  metastable  configuration,  may  be  occupied,  is  very  much  smaller,  of  the 
order  10"8  sec. 

3<>  Ann.  Physik,  45,  pp.  625-56  (1914). 


74  ORIGIN  OF  SPECTRA 

coplanar  orbit,  helium  should  resemble  lithium  and  might  therefore  be 
expected  to  be  capable  of  forming  compounds.  Franck  and  Reiche 
have  suggested  several  means,  some  involving  processes  of  this  type,  by 
which  the  electron  once  in  the  2  s  orbit  can  return  to  normal  without 
emitting  the  monochromatic  wave  number  1  S  —  2  s.  At  the  present 
time,  however,  most  of  these  hypotheses  are  highly  speculative  and 
admitting  the  above  general  conclusions,  the  transitions  from  either 
2  s  or  2  S  to  normal,  in  the  absence  of  a  strong  field,  are  not  satisfactorily 
explained. 

Kemble31  and  more  recently  Van  Vleck32  have  questioned  the  possibil- 
ity of  identifying  the  1  S  state  with  the  crossed  orbit  system  described, 
so  that  Bohr's  new  computations  of  such  orbits  will  be  awaited  with 
the  greatest  interest. 

THE  HYDROGEN  MOLECULE 

Bohr33  proposed  a  model  of  the  hydrogen  molecule  consisting  of 
two  nuclei  each  of  unit  positive  qharge,  with  two  electrons  revolving 
in  the  same  circular  orbit,  the  plane  of  which  is  symmetrically 
located  perpendicular  to  the  line  joining  the  nuclei.  The  dimensions 
are  fixed  by  the  electric  forces  and  the  condition  that  each  electron 
has  one  unit  of  angular  momentum.  The  total  energy  of  such  a 
configuration  is  readily  found  to  be  —  2.20  Nhc  ergs.  Referring  to 
Equation  (3)  or  (17)  the  energy  of  two  normal  hydrogen  atoms  is 
—  2  Nhc  ergs.  The  difference  in  these  two  values  accordingly  should 
give  the  work  necessary  to  dissociate  a  hydrogen  molecule  into  neutral 
atoms.  This  amounts  to  0.20  Nhc  ergs  or  2.7  volts.  Bohr  shows  that  a 
configuration  for  the  molecular  positive  ion,  consisting  of  the  two  nuclei 
and  a  single  electron  revolving  about  the  line  between  them,  is  unstable 
and  hence  the  removal  of  one  electron  from  the  molecule  may  result  in 
its  dissociation  and  the  production  of  a  neutral  atom  and  an  ionized 
atom.  The  total  energy  for  the  latter  state  is  —  1.00  Nhc  ergs.  The 
work  required  to  ionize  the  molecule  in  this  manner  is  accordingly  (2.20- 
1.00)  Nhc,  which  is  equivalent  to  16.2  volts. 

This  configuration  of  the  hydrogen  molecule  must  be  rejected  for 
the  following  and  other  reasons. 

(1)  Such  a  molecule  would  be  paramagnetic,  while  hydrogen  is 
known  to  be  diamagnetic. 


«  Phil.  Mag.,  42,  p.  123  (1921). 
a*  Phys.  R.,  19,  pp.  419-20  (1922). 
»«  Phil.  Mag.,  26,  pp.  857-75,  (1913). 


IONIZATION  AND  RESONANCE  POTENTIALS 


75 


(2)  Langmuir's34  experimental  determination  of  the  heat  of  dis- 
sociation is  84000  cal/mol  or  3.6  volts  per  molecule.35 

(3)  Positive  ray  analysis  shows  the  existence  of  positive  molecular 
ions. 

The  Bohr-Sommerfeld  theory  of  the  structure  of  the  hydrogen  atom, 
on  the  other  hand,  is  satisfactory,  as  the  many  remarkable  experimental 
confirmations  of  the  series  spectra  and  fine  structure  testify.  As  illus- 
trated by  Figure  4,  the  ionization  potential  of  the  atom  should  be  13.54 
volts  and  the  resonance  potential  10.16  volts,  corresponding  to  the 
convergence  frequency  and  first  line  respectively  of  the  Lyman  series. 

Measurements  of  the  critical  potentials  for  hydrogen  by  different 
observers  show  wide  divergence  both  in  the  experimental  values  and  in 
their  interpretation.  The  results  of  Horton  and  Davies  and  of  the 
authors,  given  in  Table  XV,  are  somewhat  more  consistent,  showing 
two  resonance  potentials  at  10.5  and  12  to  13  volts,  a  trace  of  ionization 
at  a  slightly  higher  point  and  strong  ionization  at  16  to  17  volts.  Our 
values  would  immediately  suggest  the  following  interpretation,  on  the 
basis  of  Bohr's  theory. 


Volts 
Observed 

Type  of  Collision 

Volts 
Com- 
puted 

Observed 

Theoretical 

10.4 
12.0 
13.3 
16.0 

Strong  resonance 
Faint  resonance 
Very  faint  ionization 
Strong  ionization 

Atom:  1st  line  of  Lyman  Series 
Atom  :  2d  line  of  Lyman  Series 
Convergence  of  Lyman  Series 
Molecule:  Bohr's  configuration 

10.2 
12.0 
13.5 
16.2 

In  spite  of  this  apparent  agreement  between  theory  and  experiment 
it  is  doubtful  that  the  above  table  represents  the  correct  analysis  of  the 
data,  the  difficulty  being  in  the  accounting  for  the  presence  of  the 
quantity  of  monatomic  hydrogen  necessary  to  give  such  a  pronounced 
indication  of  a  resonance  potential  at  10.4  volts.  In  experiments  where 
a  hot  cathode  is  employed  there  will  be  only  a  slight  amount  of  thermal 
dissociation  even  for  a  wire  operated  at  2500°  C.  There  is  possibly 

"  J.  Am.  Chem.  Soc.,  34,  p.  860  (1912). 

35  Relation  between  volts  per  molecule  and  calories  per  gram  moL      The  kinetic  energy  m 
ergs  of  an  electron  which  has  fallen  through  a  field  of  x  volts  is  given  by  Equation  (66) : 
1.592  X  lO-i2  x  volts  (66) 


ergs 

one  20°  calorie  =  4.183  •  10 7  ergs 
number  of  molecules  per  gram  mol  =  6.06 
Hence  cal.  /mol  =  23070  x  volts /molecule 
and  kg  cal. /mol  =  23.07  x  volts /molecule 


1Q23 


(67) 
(68) 
(69) 
(70) 


76  ORIGIN  OF  SPECTRA 

sufficient  dissociation,  however,  to  account  for  the  weak  ionization 
observed  at  13.3  volts.  Using  pressures  of  about  0.1  to  0.2  mm  Hg 
in  a  discharge  tube  where  the  collisions  occur  over  a  space  of  1  cni,  it  is 
found  that  about  half  of  the  electrons  lose  10.4  volts  velocity  at  this 
resonance  potential.  Now  if  J%  of  the  gas  at  any  instant  had  been 
dissociated  by  the  hot  wire,  a  very  liberal  estimate,  only  one  collision 
in  one  hundred  would  have  taken  place  with  an  atom.  Hence  one  would 
conclude  that  half  of  the  electrons  collided  some  100  times  elastically 
in  this  small  distance  before  encountering  an  atom  responsible  for  the 
energy  loss  of  10.4  volts,  a  conclusion  at  variance  with  probability 
considerations.  Thus  it  appears  likely  that  the  observed  resonance 
potential  of  10.4  volts,  as  well  as  12.0  volts,  is  due  to  the  molecule. 

We  have  made  experiments  using  a  potassium  hvdride  and  potassium 
surface  as  a  photo-electric  source  of  electrons,36  instead  of  a  hot  cathode. 
Precisely  the  same  results  were  obtained,  with  the  exception  of  ioniza- 
tion at  13.3  volts,  in  regard  to  which  no  conclusion  could  be  drawn,  as 
the  sensitivity  was  not  sufficient  to  detect  this  critical  potential.  It  is 
doubtful  whether  monatomic  hydrogen  could  have  been  present  in 
such  an  apparatus,  operated  cold. 

The  possibility  of  dissociation  by  electron  impact  below  the  resonance 
potential  is  still  an  open  question,  but  even  so,  this  could  scarcely 
account  for  a  sufficient  amount  of  atomic  hydrogen  to  explain  our 
results. 

The  agreement  between  the  observed  value  of  16.0  volts  for  the 
ionization  of  the  molecule  and  that  predicted  by  Bohr's  theory  again 
must  be  of  no  significance.  Ef  ionization  of  the  molecule  results  in  a 
neutral  atom  and  an  ionized  atom,  the  ionization  potential  should  be 
13.5  +  3.6  =  17.1  volts,  on  the  basis  of  Langmuir's  determination  of 
the  work  of  dissociation.  This  disagreement  with  experiment  suggests 
the  possibility  that  a  molecular  ion  is  formed  at  this  low  voltage.  In 
support  of  such  argument  we  have  found  that  the  secondary  spectrum 
of  hydrogen  predominates  over  the  Balmer  series  below  20  volts,  and 
the  secondary  spectrum  is  usually  ascribed  to  vibrations  of  the  molecule 
or  molecular  ion. 

It  is  possible  that  the  ionization  potential  of  the  molecule  represents 
the  work  of  dissociation  plus  the  work  of  ionization  of  one  atom  minus 
the  electron  affinity  E  of  the  hydrogen  molecule.  We  then  obtain 
13.5  +  3.6  —  E-n  =  16.0  or  Eu  =  1.1  volts.  Bohr's  theoretical  com- 
putation, based  on  the  configuration  which  we  have  shown  to  be 

3«Mohler,  Foote,  and  Kurth,  Phys.  R.,  19,  p.  414  (1922). 


ION  I Z AT  ION  AND  RESONANCE  POTENTIALS          77 

objectionable,  gives  1.6  Volts.37     Further  discussion  of  the  question  of 
electron  affinity  and  dissociation  is  given  in  Chapter  VIII. 

Although  we  have  questioned  the  ascribing  of  the  10.4  volt  resonance 
potential,  observed  by  the  ordinary  methods,  to  monatomic  hydrogen 
for  the  reason  that  we  cannot  account  for  a  sufficient  quantity  of  the 
monatomic  gas,  there  has  never  been  any  doubt  as  to  the  existence  of  a 

resonance  potential   corresponding  to  v  =  N  (      —  ^     for  the  atom 


and  an  ionization  potential  corresponding  to  v  =  N,  viz.  10.2  volts  and 
13.5  volts  respectively.  The  well-known  series  relations  require  such 
critical  potentials.  Duffenback38  has  recently  assured  the  presence  of 
an  atmosphere  of  monatomic  hydrogen  by  operating  the  ionization 
chamber  in  a  tungsten  tube  furnace  at  2000  to  2500°  abs.  At  2500° 
abs  and  1  mm  pressure  98.8  per  cent  of  the  gas  is  dissociated  into  atoms . 
He  found  that  with  the  furnace  operated  cold  most  of  the  ionization 
occurred  at  about  16  volts,  but  at  the  higher  temperatures  the  current 
showed  marked  ionization  at  10.3  and  13.2  volts.  As  will  be  discussed 
in  Chapter  VI,  arcs  may  be  struck  at  the  lowest  resonance  potential,  so 
that  the  appearance  of  the  critical  potentials  10.3  and  13.2  volts  at  high 
temperature  where  considerable  dissociation  occurs  is  a  confirmation 
of  the  facts  to  be  predicted  from  the  line  spectrum  of  the  atom. 

GENERAL  REFERENCES 

Hughes,  A.  L.,  Bull.  Natl.  Res.  Coun.,  2,  pp.  127-169  (1921).  An  excellent  tabu- 
lar summary  of  the  experimental  determinations  of  critical  potentials  to  about 
March,  1921.  As  practically  all  observations  by  numerous  observers  are  listed, 
many  of  which  were  not  made  under  satisfactory  experimental  conditions,  some 
judgment  must  be  employed  in  selecting  the  most  probable  value  where  the  range 
is  wide. 

McLennan,  J.  C.,  Phys.  Soc.,  London,  31,  pp.  1-29,  1918. 

Franck,  J.,  Physik.  Z.,  22,  pp.  388,  409,  441,  466,  1921. 

Gerlach,  W.,  Vieweg's  " Tagesfragen"  Number  58,  pp.  8-52  (1921).  This  con- 
tains a  bibiliography  of  one  hundred  and  thirty-three  references.  A  large  number 
of  American  and  English  papers  published  after  1916  are  omitted,  however,  on 
account  of  their  inaccessibility  at  that  time. 

37  Bohr,  Phil.  Mag.,  26,  p.  863  (1913),  shows  that  the  total  energy  of  the  neutral  hydrogen 
molecule  on  the  above  described  configuration  is  W  =  —  2.20Nhc  ergs.  The  total  energy  for 
the  same  configuration  with  three  electrons  instead  of  two  in  the  common  orbit,  the  plane  of 
which  is  perpendicular  to  the  line  joining  the  nuclei,  is  shown  to  be  W  =  -  2.32Nhc  ergs. 
Hence  an  amount  of  work  (2.32  —  2.20)Nhc  =  0.l2Nhc  ergs  must  be  done  on  the  second 
system  to  reduce  the  molecular  ion  to  the  normal  state.  This  is  equivalent  to  1.6  volts,  a 
value  which  accordingly  represents  the  electron  affinity  of  the  normal  molecule. 

58  Science  55,  pp.  210-211  (1922). 

8»Lyman,  Science,  56,  p.  167  (1922),  finds  in  helium  the  folio  wing  lines:  X  584.4,  X  537.1, 
X  522.3,  X  515.7,  and  possibly  X  600.5.  His  paper  appeared  after  this  book  was  in  page  proof, 
too  late  to  incorporate  in  the  discussion  on  page  72.  The  first  four  lines  are  members  of  a 
series  1  X  —  mP  where  1  X=  198290  and  IX  — 2  So  fifth  line  above  (approximately)  o  first 
resonance  potential.  These  observations  conflict  with  measurements  on  ionization  potential. 


Chapter  IV 
Line  Absorption  Spectra  of  Atoms 

LINE  ABSORPTION  SPECTRA  OF  NORMAL  ATOMS 

In  accordance  with  the  classical  theories  of  radiation,  as  expressed 
by  the  usual  interpretation  of  Kirchhoff's  law,  we  should  expect  all 
emission  lines  of  an  element  to  appear  as  absorption  lines1  when  a  column 
of  the  vapor  or  gas  is  viewed  against  a  source  which  emits  a  continuous 
spectrum.  Experimentally,  however,  in  any  particular  arrangement 
of  apparatus  we  find  that  only  for  certain  types  of  lines  is  absorption 
readily  observed.  The  quantum  theory  of  spectra  satisfactorily  ac- 
counts for  this  fact. 

As  a  particular  example  we  shall  consider  first  the  alkali  metals. 
For  the  normal  unexcited  atom  the  valence  or  outer  electron  lies  in  the 
1  s  orbit.  The  atom  accordingly  is  capable  of  absorbing  monochromatic 
radiation  in  quanta  of  a  frequency  or  energy  value  just  sufficient  to 
displace  the  valence  electron  to  an  outer  orbit.  Radiation  of  frequency 
corresponding  to  energy  intermediate2  to  two  outer  orbits  leaves  the  atom 
unaffected.  The  atom  is  unable  to  resonate  to  such  frequencies;  it  can- 
not absorb  them  because  there  is  no  position  of  equilibrium  which  the 
atom  could  assume  and  retain  the  energy.  It  cannot  absorb  a  portion 
of  the  energy  just  sufficient  to  reach  a  stable  configuration  beqause  the 
incident  radiation  exists  in  discrete,  indivisible  quanta  which  must  be 
absorbed  in  toto  or  not  at  all. 

By  the  Bohr  principle  of  selection  the  azimuthal  quantum  number 
in  any  interorbital  transition  of  an  electron  must  change  by  it  1  unit. 
Hence  only  those  frequencies  of  the  incident  radiation  will  be  absorbed 
which  result  in  the  ejection  of  the  valence  electron  to  orbits  for  which 
the  azimuthal  quantum  number  differs  by  unity  from  the  normal  state. 
This  requires  that  the  electron  pass  from  the  1  s  orbit  to  an  mp  orbit 
where  m  may  have  any  value  from  2  to  <x> .  Hence  only  radiation  of 

1  With  some  exceptions  of  academic  interest. 
8  For  other  cases,  see  Chapter  X. 

78 


LINE  ABSORPTION  SPECTRA 


79 


wave  number  v  =  1  s  —  mp  is  absorbed  from  the  continuous  source. 
The  long  column  of  absorbing  vapor  thus  accumulates  energy  and 
would  continue  to  increase  in  energy  until  the  valence  electron  of  every 
atom  finds  itself  in  a  p-orbit,  but  for  the  following  two  facts:  (1)  An 
atom  having  its  electron  in  a  p-orbit  or  any  other  outer  orbit  is  described 
as  an  "  excited  atom"  and  is  capable  of  absorbing  other  characteristic 
radiation.  This  interesting  phase  of  absorption  spectra  is  treated  in  a 
following  separate  section.  (2)  The  electron  once  displaced  almost 
instantly  resumes  its  normal  1  s  position. 

If  the  electron  displaced  to  the  mp  orbit  returns  to  the  1  s  orbit  in  a 
single  jump,  the  line  v  —  1  s  —  mp  is  emitted.  This  emission,  however, 
for  the  long  column  of  gas  is  spread  over  a  solid  angle  4  TT,  whereas  the 
radiation  absorbed  from  the  source  is  confined  to  the  narrow  beam 
passing  through  the  gas.  Radiation  of  frequency  v  —  I  s  —  mp  is 
accordingly  abstracted  from  the  beam  of  small  solid  angle  and  subse- 
quently, by  the  above  described  indirect  process,  scattered  in  all  direc- 
tions. The  result  is  that  along  the  line  of  sight  far  more  radiation  is 
absorbed  than  is  emitted  and  the  lines  v  —  1  s  —  mp  stand  out  as  sharp 
absorption  lines  against  the  continuous  source  and  the  scattered  radi- 
ation. 


58        55                 52             50             48                46 

FIG.  12.     Principal  series  lines  of  sodium  from  m  =  46  to  58,  observed  as  absorpti 

lines. 

In  general  if  1  s  or  1  S  represents  the  normal  orbit  of  the  electron 
in  the  unexcited  atom,  we  should  expect  to  observe  as  absorption  lines 
the  wave  numbers  v  =  1  s  —  mp  for  the  alkalis;  1  S  —  mp2  and  IS  — 
mP  for  the  metals  of  Group  II  of  the  periodic  table  and  similarly  for  the 
other  groups.  Lines  in  emission  series  which  converge  at  1  s  or  1  5, 
when  the  orbits  corresponding  to  these  frequencies  represent  the  normal 
state,  should  be  absorption  lines,  characteristic  of  the  normal  atom. 

The  experimental  verifications  of  this  simple  theory  are  conclu- 
sive. Wood  and  Fortrat,3  using  in  effect  a  train  of  thirteen  60° 
quartz  prisms,  have  examined  the  absorption  spectra  of  a  long  column 
(3  meters:  20  meters  recommended)  of  sodium  vapor  of  fairly  low  den- 

3  Wood  and  Fortrat,  Astrophys.  J.,  43,  pp.  73-80  (1916). 


80  ORIGIN  OF  SPECTRA 

sity.  The  only  absorption  lines  appearing  belonged  to  the  principal 
series  Is  —  mp.  These  were  observed  to  m  =  58,  fifty-seven  pairs, 
although  the  resolution  was  not  sufficient  to  separate  the  pairs  beyond 
m  =  8.  The  last  thirteen  observed  members  of  the  series  are  indicated, 
on  a  wave-length  scale,  by  Figure  12.  The  wave-length  corresponding 
to  the  convergence  frequency  lies  to  the  left  of  the  line  m  =  58  about 
the  distance  equal  to  the  length  of  the  portion  of  the  series  illustrated. 
On  this  scale  the  D-lines  would  lie  to  the  right  a  distance  of  1100  feet. 
Line  m  =  46  differs  in  wave-length  from  line  m  =  58  by  about  one 
Angstrom  unit. 

Figure  13  illustrates  the  line  absorption  spectrum  of  sodium.  The 
upper  spectrogram  is  from  a  negative  made  by  Dr.  G.  R.  Harrison  and 
shows  the  absorption  of  the  second,  third  and  fourth  members  of  the 
principal  series.  At  low  vapor  pressure  these  lines  are  very  sharp. 
If  the  pressure  is  increased,  higher  terms  are  brought  out,  but  the  absorp- 
tion of  the  first  members  widens  into  broad  bands,  as  shown  by  the 
lower  spectrogram  made  by  Prof.  Wood.  The  central  spectrogram, 
also  Wood's,  shows  the  line  absorption  clearly,  nearly  to  the  head  of  the 
series.  We  have  marked  twenty-one  terms,  but  many  more  were  readily 
visible  in  the  negative.  The  emission  lines  in  these  illustrations  are 
due  to  the  cadmium  or  aluminum  spark  in  air  employed  as  a  source. 

The  exact  physical  significance  of  the  broadening  of  the  lines  at 
high  pressure  has  not  been  satisfactorily  interpreted  by  the  quantum 
theory.4  The  necessity  for  employing  high  pressure  in  order  to  bring 
out  higher  terms  is  to  be  expected.  The  chance  that  an  electron  be 
displaced  to  say  the  58th  orbit  is  small  when  there  are  so  many  orbits 
of  nearly  identical  energy  value.  By  increasing  the  pressure  the  number 
of  atoms  is  increased  with  a  proportionate  change  in  the  probability 
of  a  displacement  to  any  individual  orbit,  and  the  resulting  absorption 
of  the  corresponding  line.  The  same  effect  might  be  produced  by  in- 
creasing the  length  of  the  column  of  vapor.  The  phenomenon  at  high 
pressure  is,  however,  complicated  possibly  by  the  interpenetration, 
or  certainly  by  the  perturbations,  of  orbits  of  electrons  in  neighboring 
atoms. 

Wood's  work  on  sodium  has  been  extended  to  the  other  alkali  vapors 
by  Bevan.5  In  this  manner  terms  of  the  principal  series  were  obtained 
as  absorption  lines  to  m  =  25  for  potassium,  m  =  26  for  rubidium, 
m  =  22  for  caesium  and  m  =  28  for  lithium. 

4  See  page  91. 

s  Proc.  Roy.  Soc.  Lond.,  83,  pp.  421-28  (1910),   85,  pp.  54-8  (1910). 


2680 


Z853 


3303 


FIG.  13.     Absorption  spectrum  of  sodium,  showing  absorption  of  principal  series 
lines.     The  bright  lines  are  due  to  the  source  of  light. 


SOB 


215°C 


236 


250 


275 


360 


FIG.  ,  14.     Absorption  spectrum  of  mercury  showing  the  absorption  line  X  2537, 
1 S  —  2  p2.     The  emission  lines  are  due  to  the  source  of  light. 


80  C 


FIG.  14A.     Absorption  of  mercury  X  2537.     The  continuous  spectrum  is  produced 
by  an  aluminum  spark  under  water.     Tungsten  electrodes  are  still  better. 


Cs 


8943.46' 


FIG.  15.     Reversals  of  the  first  pair  of  the  principal  series  for  the  alkalis.     The  illus- 
trations have  been  prepared  on  the  same  scale  of  wave-lengths.  , 


SOD 


* 


FIG.  15A.     Illustrating  the  practically  complete  absorption  of  rare  mercury  vapor  for 
the  resonance  radiation  X  2537. 


LINE  ABSORPTION  SPECTRA  81 

The  important  series  converging  at  1  S  for  the  metals  of  Group  II 
are  mainly  confined  to  the  ultra-violet.  Wood  first  showed  that  the 
mercury  line  1  S  —  2  p%,  X  =  2537,  is  strongly  absorbed  by  a  column 
of  mercury  vapor.  Figure  14,  by  Wood,  illustrates  this  absorption  very 
clearly.  At  low  pressure,  the  absorption  is  very  sharply  defined,  but  as 
the  pressure  of  the  vapor  is  increased,  by  increasing  the  temperature  as 
indicated,  the  line  widens  into  a  band.  The  absorption  of  this  line  is 
now  a  matter  of  common  experience  in  the  operation  of  a  quartz  mercury 
vapor  lamp.  If  the  lamp  is  overheated,  as  was  first  pointed  out  by 
Wood,  its  actinic  effect  is  greatly  reduced  on  account  of  the  absorption 
of  X  2537  by  the  dense  vapor.  A  photograph  of  the  arc  under  such 
conditions  shows  almost  complete  absence  of  this  line.  On  account  of 
the  continuous  spectrum  which  is  produced  with  strong  current  and 
high  temperature  X  2537  may  appear  as  a  strong  reversal  against  the 
faint  background  of  the  continuous  emission  spectrum. 

Wood  and  Guthrie6  found  absorption  in  cadmium  vapor  for  the 
lines  1  S  -  2  p2,  X  3260  and  1  S  -  2 '  P,  X  2288.  McLennan  and  Ed- 
wards7 have  demonstrated  that  the  mercury  line  1  S  —  2  P,  X  1849,  is 
entirely  absorbed  by  a  column  of  rare  mercury  vapor,  but  did  not  succeed 
in  obtaining  it  as  a  reversal  against  a  continuous  background.  The 
experimental  difficulty  here  is  in  producing  a  suitable  continuous  source 
of  ultra-violet  light.  The  best  method  so  far  devised8  is  the  use  of  an 
aluminum  or  preferably  tungsten  spark  gap  immersed  in  water  and 
excited  by  a  very  high  voltage,  using  a  Tesla  coil,  auxiliary  air  gap  and 
capacity.  This  gives  a  continuous  spectrum  throughout  the  visible 
and  in  the  ultra-violet  at  least  to  the  limit  of  the  quartz  spectrograph. 
It  is  obviously  not  suitable  however  for  work  with  the  vacuum  spectro- 
graph. For  this  range  the  Lewis9  method  employing  hydrogen  offers 
a  little  hope,  but  its  use  is  necessarily  restricted.  One  will  readily 
appreciate  the  almost  insurmountable  difficulties  in  the  determination 
of  absorption  spectra  of  metallic  vapors  below  X  2000. 

McLennan  and  Edwards  besides  corroborating  Wood's  work  ob- 
served absorption  and  complete  reversal  against  a  brighter  background, 

6  Astrophys.  J.,  29,  p.  211  (1909). 

7  Phil.  Mag.,  30,  pp.  695-700  (1915). 

8  The  electrical  arrangement  is  described  by  Howe,  Phys.  R.,  8,  p.  681  (1916).    Fig.  14A 
shows  the  beautiful  continuous  spectrum  which  is  easily  obtained.    If  only  the  central  portion 
of  the  spark  is  employed  practically  no  trace  of  emissidn  lines  is  present.    In  this  spectrogram 
Dr.  Meggers  and  the  authors  were  endeavoring  to  obtain  the  line  absorption  spectrum  of 
arsenic  vapor.    This  was  unsuccessful,  but  the  absorption  of  the  mercury  line  X  2537  is  very 
pronounced,  arising  in  the  mercury  which  was  present  with  the  arsenic  vapor.    The  mercury 
emission  spectrum  is  also  shown  for  comparison.     More  recent  descriptions  of  the  spark 
apparatus  are  given  in  "  Transmissivity  of  Food  Dyes."     Bur.  Standards  Sci.  Paper  No.  440. 

9  Science,  41,  p.  947  (1915);    Phys.  R.,  16,  p.  367  (1920).      Hulburt,  Astrophys.  J.,  42, 


82  ORIGIN  OF  SPECTRA 

in  rare  zinc  vapor,  of  the  zinc  line  1  S  —  2  p2,  X  3076  and  complete 
absorption  of  1  S  -  2  P,  X  2139. 

McLennan10  using  a  column  of  magnesium  vapor  obtained  reversal 
of  the  line  1  S  —  2  P,  X  2852,  and  showed  the  presence  of  absorption 
for  1  S  —  3  P,  X  2026.  For  some  unexplained  reason  he  could  not 
detect  absorption  of  the  fundamental  line  1  S  —  2  p2,  X  4571. 

King's11  work  on  furnace  spectra  shows  that  fundamentally  important 
lines  are  readily  absorbed  and  may  appear  as  reversals  against  the 
brighter  background  of  the  furnace  walls,  for  example  X  4227, 1  S  —  2  P, 
of  calcium.  King  states  that  in  general,  for  all  metals  the  strong  absorp- 
tion lines  are  those  which  are  excited  as  emission  lines  at  low  temperature. 
Among  these  latter,  as  will  appear  in  Chapter  VII,  are  to  be  found  the 
fundamental  lines  of  series  converging  at  1  S  or  1  s,  at  least  insofar  as 
the  spectral  region  investigated  covers  that  embraced  by  these  series. 

REVERSED  LINES 

The  spectrum  of  a  material  obtained  in  an  ordinary  arc  is  in  general 
composed  of  emission  lines.  However,  under  certain  conditions  lines 
are  reversed,  appearing  black  against  the  brighter  background.  An 
example  of  this  is  shown  by  Figure  15,  prepared  by  Meggers,  for  the  first 
pair  in  the  principal  series  of  each  of  the  alkalis.  The  reversed  portion, 
which  appears  black,  is  much  narrower  than  the  emission  line,  showing 
in  the  reproduction  as  a  white  band.12  Generally  absorption  lines  are 
more  nearly  monochromatic  than  the  corresponding  emission  line,  in 
part  because  of  the  smaller  £>oppler  effect  and  lesser  pressure  of  the 
cooler  vapor,  but  also  for  other  reasons  which  have  not  been  satis- 
factorily explained.  The  reversal  is  due  to  absorption  of  the  emitted 
light  by  the  zone  of  cooler  vapor  surrounding  the  arc.  In  the  illus- 
tration given  the  emission  line  for  caesium  is  exceptionally  broad. 
Frequently,  however,  the  emission  lines  are  narrow  and  the  reversal 
may  then  almost  or  even  completely  cover  the  emission.  Reversals 
are  found  even  in  flame  spectra.  A  narrow  reversal  of  the  D -lines 
against  the  broader  background  of  the  emission  spectrum  is  readily 
observed  in  a  long  train  of  bunsen  burners  fed  with  salt. 

Probably  reversals  in  the  arc  can  be  obtained  for  all  lines  of  series 
converging  at  1  s  or  1  S.  The  observation  of  a  reversal,  however,  does 
not  indicate  that  the  line  belongs  to  these  series.  Among  the  thousands 

"McLennan,  Proc.  Roy.  Soc.,  95,  pp.  273-9  (1919). 
"  Astrophys.  J.,  51,  pp.  13-22  (1920). 

12  It  is  of  interest  that  the  square  root  of  the  doublet  separations  for  the  alkalis  v 
plotted  against  atomic  number  gives  an  approximately  straight  line. 


LINE  ABSORPTION  SPECTRA  83 

of  reversals  listed  in  the  spectroscopic  tables  will  be  found  all  types  of 
lines,  including  those  belonging  to  subordinate  and  combination  series, 
series  converging  at  2  s,  etc.,  the  explanation  of  which  is  given  in  the 
section  on  excited  atoms  and  in  Chapters  VI  and  VII.  On  the  other 
hand  by  careful  consideration  of  reversed  lines  considerable  information 
may  be  derived  concerning  series  relations.  Thus  with  copper  we 
find  a  strong  reversal  of  the  pair  X  3248  and  X  3275,  which  fact  combined 
with  our  somewhat  unsatisfactory  knowledge  of  the  series  relations 
for  this  element  enables  us  to  predict  with  a  fair  degree  of  certainty 
that  this  is  the  pair  1  s  —  2  p  which  determines  the  value  of  the  resonance 
potential.  For  the  same  reason  we  are  led  to  suspect  that  X  2428  is  a 
member  of  the  principal  series  of  gold,  and  is  likely  the  term  Is  —  2  pi, 
although  the  series  relations  are  entirely  unknown.  The  fact  that  all 
the  lines  of  Paschen's  principal  series  of  thallium  are  so  readily  reversed 
in  the  arc  is  a  strong  argument  for  assigning  the  notation  1  s  to  the 
convergence  frequency  instead  of  2  s,  as  suggested  in  the  chapter  on 
ionization  potential.  In  this  particular  case,  however,  the  vapor  may  be 
" excited"  by  the  high  temperature,  as  discussed  in  Chapter  VII.  Under 
such  conditions  the  fundamentally  important  lines  should  be  suppressed 
both  in  emission  and  absorption,  especially  so  since  the  resonance  po- 
tential is  extremely  low.  The  work  of  Wood  and  Guthrie13  on  absorp- 
tion of  thallium  vapor  is  suggestive  but  inconclusive  and  should  be 
repeated  using  as  long  a  column  of  vapor  at  as  low  a  temperature  as 
practicable. 

McLennan  and  Young14  have  made  an  investigation  of  the  arc  re- 
versals for  calcium,  strontium  and  barium.  They  observed  the  first 
six  lines  of  the  series  1  S  —  mP  as  reversals  in  calcium,  ten  lines  of  this 
series  in  strontium  and  nine  lines  in  barium.15 

One  finds  in  the  spectroscopic  tables  that  at  least  the  first  term  of  the 
series  1  S  —  2  P  and  1  S  —  2  p%  has  been  observed  reversed  for  most  of 
the  elements  of  Group  II.  In  Table  XVI  are  listed  several  of  the  early 
members  of  these  series.  A  few  of  these  lines  are  merely  computed 
values,  having  been  unobserved  as  yet  either  in  emission  or  absorption. 
In  the  last  column,  A  denotes  that  the  line  has  been  observed  as  an 
absorption  line,  using  a  long  column  of  vapor;  R  as  a  reversal  in  an  arc; 
K  as  a  reversal  in  furnace  spectra,  and  F  as  an  emission  line  in  flame 
spectra.  It  is  noted  that  the  wave-lengths  of  many  of  the  lines  are  less 
than  2000  A.  These  accordingly  can  be  best  studied,  for  absorption, 

13  Astrophys.  J.,  29,  p.  211  (1909).  "  Proc.  Roy.  Soc.  95,  pp.  273-9  (1919). 

15  Two  of  these  were  assigned  entirely  incorrect  wave-lengths,  viz.,  IS  -  3P  and  IS  -  4P 
for  barium. 


84 


ORIGIN  OF  SPECTRA 


as  reversals  in  arcs.  A  suggested  method  suitable  for  the  vacuum 
spectograph  is  to  employ  a  very  long  vertical  tube  with  a  Wehnelt  cathode 
arc  at  the  bottom.  The  metal  is  boiled  at  the  bottom  and  condensed 
in  the  upper  part  of  the  tube,  at  the  top  of  which  is  mounted  the  spectro- 
graph,  sufficiently  distant  to  prevent  contamination.  The  emission 
lines  will  be  broad  on  account  of  the  higher  pressure  at  the  bottom  of 
the  tube,  thus  furnishing  a  background  for  the  absorption  lines  produced 
by  the  long  column  of  rarer  vapor.  There  is,  however,  still  a  splendid 
field  for  work  at  wave-lengths  longer  than  2000  A.  especially  with 
elements  of  other  groups  of  the  periodic  table. 

TABLE  XVI 

IMPORTANT  (FROM  STANDPOINT  OF  ATOMIC  STRUCTURE)  SERIES  LINES 
FOR  METALS  OF  GROUP  II.     COMPILED  BY  F.  A.  SAUNDERS 


Element 

Notation 

i/ 

X  (vacuum) 

X  (air) 

Remarks16 

Me  . 

18 

61672 

1622 

21871 

4572 

4571 

FK 

1  <$  _  3  p2 

47853 

2090 

1  S  —  4  pz 

54253 

1843 

1  S  —  5  pz 

57020 

1754 

1S-2P 

35051 

2853 

2852 

AFRK 

1S-3P 

49347 

2026 

RK 

1S-4P 

54703 

1828 

Ca  

IS 

49305 

2028 

15210 

6575 

6573 

K 

1  $  —  3  pz 

36555 

2736 

2735 

1  S  —  4  pz 

42519 

2352 

1  S  —  5  7)2 

44962 

2224 

1S-2P 

23652 

4228 

4227 

RKF 

1S-3P 

36732 

2723 

2722 

K 

1S-4P 

41679 

2399 

2399 

RK 

1S-5P 

43933 

2276 

2275 

RK 

Zn    . 

1£ 

75767 

1318 

1  S  -  2  pz 

32502 

3077 

3076 

ARFK 

1  S  —  3  2?2 

61274 

1632 

1  >S  —  4  £>2 

68081 

1469 

1  $  _  5  p2 

70982 

1409 

._.. 

1S-2P 

46745 

2139 

2139 

ARK 

1S-3P 

62902 

1590 

1>S-4P 

68608 

1458 

IS  -5P 

71215 

1404 

16  A  denotes  that  the  line  has  been  observed  as  an  absorption  line  using  a  long  column  of 
rare  vapor.     Continued  on  page  85. 


LINE  ABSORPTION  SPECTRA 


85 


TABLE  XVI  —  Continued 

IMPORTANT  (FROM  STANDPOINT  OF  ATOMIC  STRUCTURE)  SERIES  LINES 
FOR  METALS  OF  GROUP  II.     COMPILED  BY  F.  A.  SAUNDERS 


Element 

Notation 

V 

X  (vacuum] 

X  (air) 

Remarks16 

Sr  

18 

45926 

2177 

lS-2p2 

14504 

6895 

6893 

K 

1  S  -  3  p2 

33869 

2953 

2952 

lS-4p2 

39426 

2536 

IS  -2P 

21698 

4609 

4607 

RFK 

1  S  -  3  P 

34098 

2933 

2932 

K 

1S-4P 

38907 

2570 

2570 

RK 

1S-5P 

41172 

2429 

2428 

RK 

Cd 

IS 

72539 

1379 

IS  -2p2 

30656 

3262 

3261 

ARFK 

lS-3p2 

58462 

1711 

!S-4p2 

65027 

1538 

!S-5p2 

67842 

1474 

IS-2P 

43692 

2289 

2288 

ARFK 

. 

1S-3P 

59906 

1669 

1S-4P 

65494 

1527 

1S-5P 

68056 

1469 

Ba  

IS 

42029 

2379 

1  S  -  2  p2 

12637 

7913 

7911 

K 

lS-3p2 

30815 

3245 

3244 

K 

1  S  -  4  p2 

35892 

2786 

IS-2P 

18060 

5537 

5535 

RFK 

IS-ZP 

32547 

3072 

3072 

RK 

1S-4P 

36990 

2703 

2703 

RK 

1S-5P 

38500 

2597 

2597 

RK 

Hg.  , 

IS 

84178 

1188 

lS-2p2 

39413 

2537 

2537 

ARFK 

!S-3p2 

69656 

1436 

1  S  -  4  p2 

76464 

1308 

1  S  -  5  p2 

79410 

1259 

IS-2P 

54066 

1850 

AK 

IS-ZP 

71291 

1403 

1S-4P 

78810 

1269 

1S-5P 

79961 

1251 

16  (Continued)   R  denotes  that  the  line  has  been  observed  as  a  reversal  in  an  arc. 

K  denotes  that  the  line  has  been  observed  as  an  absorption  line  in  furnace  spectra,  i.e., 
reversed  against  the  bright  walls  of  the  furnace. 

F  denotes  that  the  line  has  been  observed  as  an  emission  line  in  a  flame. 

For  relation  between  X  (vac)  and  X  (air)  see  data  of  Meggers  and  Peters,  Smithsonian 
Tables,  7th  Ed.,  p.  293.  Also  Bui.  Bur.  Standards,  14,  p.  731  (1918). 


86  ORIGIN  OF  SPECTRA 

RESONANCE  RADIATION 

As  stated  earlier,  the  mechanism  of  line  absorption  of  vapors  involves 
the  re-emission  of  the  radiant  energy  absorbed.  This  re-emitted  light, 
called  resonance  radiation,  has  been  studied  in  considerable  detail  for 
sodium  and  mercury.17  If  a  bulb  of  pure  sodium  vapor  at  low  pressure 
is  illuminated  by  a  beam  of  light  from  a  sodium  flame  or  vacuum  arc, 
the  vapor  will  diffusely  emit  radiation  consisting  of  only  the  two  D- 
lines,  1  s  —  2  pi  and  1  s  —  2  p2.  At  very  low  pressure,  less  than  that 
corresponding  to  saturation  at  150°  C,  the  entire  bulb  is  filled  with  a 
faint  glow.  As  the  pressure  is  increased  the  diffusely  emitted  light 
becomes  concentrated  near  the  place  of  incidence  of  the  exciting  beam 
of  radiation,  and  at  250°  C,  pressure  about  0.01  mm,  is  confined  to  the 
extreme  surface. 

These  phenomena  show  that  the  effective  part  of  the  incident  radi- 
ation is  absorbed  in  a  very  thin  layer  of  the  vapor  at  the  higher  temper- 
ature while  at  lower  temperatures  and  pressures  the  radiation  penetrates 
the  bulb  and  is  passed  on  from  atom  to  atom  throughout  the  volume. 

Analysis  of  the  emitted  light  by  the  interferometer  shows  that  the 
entire  width  of  the  lines,  about  0.03  A,  may  be  accounted  for  by  the 
Doppler  effect  alone  of  the  vapor  at  this  comparatively  low  temperature. 
Only  a  portion  of  the  exciting  D-radiation  is  absorbed  so  that  the  beam 
passing  through  the  vapor  shows  a  very  narrow  absorption  line  in  the 
center  of  each  of  the  broad,  transmitted  D-lines. 

Strutt18  has  found  that  the  sodium  doublet  1  s  —  3  p,  X  3303,  like- 
wise excites  resonance  light.  In  this  case  the  emitted  radiation  consists 
of  both  D-lines  and  radiation  of  the  frequency  absorbed,  X  3303.  This 
is  in  accord  with  the  quantum  theory.  Absorption  of  a  quantum  of 
radiation  of  wave-length  X  3303  ejects  an  electron  from  the  1  s  orbit  to 
either  the  3  pi  or  3  p2  orbit.  This  energy  may  be  given  up  either  by  a 
direct  return  to  1  s  with  the  emission  of  1  s  —  3  p  or  indirectly  by  a 
transition  to  2  p  and  from  there  to  1  s,  the  latter  step  involving  the 
emission  of  the  D-lines..  The  Bohr  principle  of  selection  shows  that, 
in  the  absence  of  a  disturbing  field,  a  direct  fall  from  3  p  to  2  p  with  the 
emission  of  2  p  —  3p  should  not  occur,  a  fact  confirmed  by  Strutt.  The 
transition  between  these  two  orbits  must  be  made  through  either  the 
2  s  or  3  d  orbit  as  an  intermediate  stage,  as  shown  by  Figure  9.  The 
following  table  illustrates  the  various  steps  involved  as  a  consequence 

17  Cf.  Wood's  "  Physical  Optics,"  2d  Ed.    The  discovery  and  a  great  part  of  the  develop- 
ment of  this  subject  is  due  to  Wood  and  his  co-workers. 
"Proc.  Roy.  Soc.,  96,  pp.  272-86  (1919). 


LINE  ABSORPTION  SPECTRA 


87 


of  the  absorption  of  1  s  —  3  pi.  A  similar  table  may  be  prepared  for  an 
initial  absorption  of  1  s  —  3  p2  in  which  all  steps  from  d  on  are  the  same 
as  here  given.  Absorption  of  1  s  —  3  p\  accordingly  may  be  followed 
by  emission  through  the  successive  stages  b  or  c,  e,  i,  or  d,  g,  i  or  d,  h,  j, 
etc.  With  many  atoms  returning  to  normal  by  different  paths,  all  of  the 
lines  given  in  this  table  may  be  emitted.  Strutt's  observation  that 
both  D-lines  as  well  as  1  s  —  3  p  are  emitted  when  the  exciting  radiation 
is  1  s  —  3  p  is  accordingly  confirmed  by  the  theory.  The  reason  that 
Strutt  did  not  observe  the  other  lines  listed  is  because  they  all  lie  in  the 
infra-red. 


TABLE  XVII 


Step 

Position  of  Valence 
Electron 

Radiation 

Wave-length 
in  A 

Initial 

Final 

Notation 

Remarks 

a 

Is 

3P1 

Is  -3  pi 

absorbed 

3302.5 

b 

3pi 

Is 

Is  -  3pi 

radiated 

3302.5 

c 

3  pi 

3d 

3d  -3pi 

u 

90480. 

d 

3pi 

2s 

2s  —  3pi 

u 

22056.9 

e 

3d 

2  pi 

2  Pl-  3d 

u 

8196.1 

f 

3d 

2p2 

2p2-3d 

11 

8184.5 

g 

2s 

2pi 

2  pi-  2s 

It 

11404.2 

h 

2s 

2p2 

2p2-2s 

11 

11382.4 

i 

2pi 

Is 

l«-2pi 

11 

5890.2 

j 

2p2 

Is 

1  s  -  2  p2 

It 

5896.2 

If  sodium  vapor  is  excited  by  one  of  the  D-lines  alone,  we  should 
expect  that  only  this  line  would  appear  in  the  resonance  radiation,  since 
a  transition  from  2  pi  to  2  p2  involving  an  emission  of  2  p2  —  2  pi  is 
contrary  to  the  Bohr  principle  of  selection  and  a  transition  from  2  p2 
to  2  pi  requires  additional  energy.  Wood  and  Dunoyer19  concluded 
that  resonance  radiation  excited  by  one  D-line  consisted  of  that  D-line 
alone.  Wood  and  Mohler,20  however,  later,  showed  that  this  was  true 
only  at  extremely  low  pressure.  If  the  pressure  of  the  sodium  vapor  is 
increased  or  if  hydrogen  is  added,  both  D-lines  appear  when  the  excita- 
tion is  by  either  DI  or  D2  alone.  It  is  possible  that  the  principle  of 
selection  is  broken  down  at  high  pressure  by  the  disturbing  field  of 

i»Phil.  Mag.,  27,  p.  1018  (1914). 
2«Phys.  R.,  11,  p.  70  (1918). 


88  ORIGIN  OF  SPECTRA 

neighboring  atoms.  In  such  case  by  excitation  with  1  s  —  2  pi  the 
infra-red  line  2  p2  —  2  plt  \  590  n  (1/17  cm),  may  be  emitted  with  the 
subsequent  emission  of  1  s  —  2  p2-  For  the  same  reason  excitation  by 
1  s  —  2  p2  may  be  followed  by  absorption  of  2  p2  —  2  pi  from  the  con- 
tinuous emission  spectrum,  black-body  distribution,  of  the  walls  of  the 
vessel  or  room.  This  would  eject  the  electron  to  the  2  pi  orbit,  thus 
permitting  the  subsequent  emission  of  1  s  —  2  pt.  It  is  also  possible, 
when  we  are  concerned  with  such  extremely  minute  quantities  of  energy 
as  are  represented  by  quanta  of  wave-length  1/17  cm,  that  atomic 
collisions  may  play  an  important  role  and  .that  the  transfer  of  the  electron 
between  2  pi  and  2  p2  is  the  direct  result  of  slightly  inelastic  collision. 
Under  such  circumstances  the  principle  of  selection  would  not  be 
violated. 

Mercury  vapor  at  low  pressure  shows  resonance  radiation  for  the 
line  X  2537,  1  S  —  2  p2.  No  investigation  has  been  made  with  excitation 
by  other  fundamental  lines,  1  S  —  3  p2,  1  S  —  2  P,  etc.,  since  they  lie  in 
an  inconvenient  spectral  region,  as.  shown  by  Table  XVI.  If  the  width 
of  the  resonance  line  is  due  entirely  to  the  Doppler  effect,  we  have  for  the 
vapor  at  room  temperature: 

width  of  line  =  0.86  •  10~6X  VT/M  =  0.0026  Angstrom. 

Hence  to  observe  the  absorption  of  this  line  or  the  reversal  of  such  a 
narrow  line  against  the  broad  emission  spectrum  should  require  high 
resolving  power.  The  pressure  of  mercury  vapor  at  room  temperature  is 
about  0.001  mm  Hg;  at  60°  C,  0.02  mm;  at  100°  C,  0.28  mm.  This  small 
variation  in  temperature  does  not  materially  change  the  Doppler  effect, 
yet  at  even  60°  C  the  absorption  of  a  short  column  of  mercury  vapor  may 
be  readily  observed  with  a  prism  spectrograph  and  a  pronounced  reversal 
obtained  against  a  continuous  source,  similar  to  the  reversals  shown  in 
Figure  14.  It  is  an  experimental  fact  that  absorption  of  X  2537  by  mercury 
vapor  at  20°  C  cannot  be  detected  with  an  ordinary  prism-spectrograph, 
because  of  the  insufficient  resolution.  Yet  a  very  short  column  of  rare 
vapor  is  opaque  to  a  portion  of  this  line,  a  fact  simply  and  clearly  dem- 
onstrated by  Wood.  A  saucer  containing  mercury  at  room  temper- 
ature was  photographed  with  a  quartz-lens  camera  against  the  resonance 
radiation  emitted  by  a  bulb  of  mercury  vapor,  which  was  excited  by  a 
beam  of  radiation  X  2537.  The  photograph  showed  the  opaque  clouds 
of  the  vapor  rising  over  the  dish.  If  the  photograph  is  made  with  an 
ordinary  source  of  X  2537,  many  times  broader  than  the  absorption  line, 
the  vapor  above  the  saucer  appears  transparent. 


LINE  ABSORPTION  SPECTRA  89 

Figure  15  A  obtained  by  Wood21  shows  the  shadow  cast  by  a  quartz 
bulb  filled  with  mercury  vapor  at  room  temperature  when  illuminated 
by  the  mercury  resonance  radiation.  The  opacity  of  the  extremely 
rare  vapor  to  this  radiation  is  readily  apparent,  the  entire  bulb  appearing 
black.22 

If  a  beam  of  X  2537  from  an  ordinary  mercury  arc  passes  through  a 
column  of  mercury  vapor  at  low  pressure  the  scattered  light  is  not  con- 
fined to  the  geometrical  boundary  of  the  beam,  but  as  mentioned  earlier 
for  sodium,  is  diffusely  radiated  throughout  the  vapor.  Wood23  has 
measured  the  rate  at  which  the  intensity  decreases  in  mercury  vapor  at 
0.001  mm  Hg  pressure  in  a  direction  at  right  angles  to  the  geometrical 
boundary  of  the  beam  as  follows : 


Distance 

Relative  Intensity 

0.0  mm 

1/1 

0.5 

1/3 

1.5 

1/6 

2.5 

1/10 

3.5 

1/30 

These  data  probably  give  an  approximate  measure  of  the  absorption 
coefficient  of  the  vapor  for  the  resonance  radiation.  For  example, 
0.5  mm  of  mercury  vapor  at  0.001  mm  Hg  pressure  may  reduce  the 
intensity  of  a  beam  of  resonance  radiation  to  1/3  its  initial  value.  It 
is  unfortunate  that  the  value  of  the  absorption  constant,  the  importance 
of  which  will  appear  in  Chapter  VI,  has  not  been  measured  by  a  more 
direct  method,  but  very  likely  the  experimental  difficulties  would  be 
considerable. 

An  exact  definition  of  resonance  radiation  is  difficult  to  formulate. 
Originally  the  term  referred  to  the  radiation  of  the,same  wave-length  as 
that  of  the  exciting  source,  emitted  by  a  vapor  which  before  the  excita- 

21  "Researches  in  Physical  Optics,"  Part  I,  Columbia  University  Press. 

22  In  a  recent  letter  R.  W.  Wood  gives  the  results,  as  yet  unpublished,  of  experiments 
on  the  intensity  of  mercury  resonance  radiation.     The  intensity  is  increased  by  the  addi- 
tion of  helium  or  argon,  although  other  gases  reduce  the  intensity  of  the  radiation  or  de- 
stroy it  entirely.    In  helium  at  33  cm,  the  radiation  is  4  times  as  strong  as  in  Hg  vapor  alone 
at  room  temperature  (.001  mm  pressure).    The  complete  explanation  of  these 'phenomena 
is  probably  quite  complicated,  but  it  has  been  shown  experimentally  that  the  increase  of  in- 
tensity by  helium  is  due  to  the  fact  that  the  spectral  range  absorbed  (out  of  the  middle  of 
the  broad  2537  exciting  line)  is  widened,  so  that  more  energy  is  diverted  from  the  primary 
beam.    This  was  proved  by  first  passing  the  exciting  beam  of  X  2537  light  through  a  cell  of 
Hg  vapor  in  vacuo.    It  was  thus  freed  of  all  frequencies  capable  of  exciting  Hg  vapor  in  vacuo ; 
however,  it  excited  powerfully  Hg  in  helium. 

23  "Researches  in  Physical  Optics, "Part  I,  p.  54. 


90  ORIGIN  OF  SPECTRA 

tion  was  in  a  normal  state.  Hence  the  D-lines  stimulated  by  the  D- 
lines  may  be  called  resonance  radiation,  while  the  excitation  of  the  D- 
lines  by  the  second  pair  of  the  principal  series  would  not  fall  within  this 
classification.  We  shall  see,  however,  in  the  following  section  that  an 
atom  having  an  electron  in  an  outer  orbity  for  example  the  2  p2  orbit, 
•is  capable  of  absorbing  the  first  line  of  a  subordinate  series  and  subse- 
quently may  re-emit  the  line  as  strictly  resonance  radiation.  Accord- 
ingly, even  if  we  rigidly  restrict  the  terminology  resonance  radiation  to 
the  emission  of  the  same  radiation  as  that  of  the  stimulating  source, 
any  line  whatever  may  be  a  resonance  line  depending  upon  the  state  of 
the  vapor.  If  the  atoms  are  in  a  normal  condition,  lines  of  the  funda- 
mentally important  series  converging  at  1  S  or  1  s  may  be  resonance 
lines.  If  the  atoms  are  "excited, "as  explained  in  the  following  section, 
lines  of  other  series  may  show  resonance  radiation.  The  phenomenon 
is  simply  a  consequence  of  absorption.  Any  line  which  is  absorbed, 
by  a  monatomic  vapor,  from  a  beam  of  radiation,  subsequently  may  be 
radiated  in  all  directions,  and  observed  as  scattered  light. 

It  may  be  that  the  definition 'of  resonance  radiation  should  be  re- 
stricted, as  advocated  by  Franck,  to  the  case  where  the  emitted  fre- 
quency is  the  only  one  possible.  This  would  require  in  general  that  the 
first  line  of  a  principal  series,  converging  at  1  S  or  1  s,  or  a  combination 
line  if  of  lower  frequency,  should  be  a  resonance  line,  for  example  Is  — 
2  p  for  the  alkalis  and  1  S  —  2  p2  for  the  alkali  earths.  Further,  since 
transitions  from  2  P  to  2  pz  in  the  absence  of  a  disturbing  field  are  con- 
trary to  the  Bohr  selection  principle,  tHe  line  1 S  —  2  P  should  be  a 
resonance  line  for  metals  of  Group  II  even  upon  the  above  restricted 
definition.  Franck  classes  the  scattered  emission  of  the  line  2  s  —  2  p 
of  helium,  X  10830,  as  resonance  radiation  because  the  2  s  state  is  a 
metastable  configuration  and  an  electron  in  the  2  p  orbit  can  give  rise 
to  the  emission  of  only  2  s  —  2  p. 

The  phenomena  of  resonance  radiation  must  not  be  confused  with 
the  fluorescence  of  metallic  vapors.  Fluorescent  spectra  are  best 
observed  with  much  greater  vapor  densities  and  with  intense  illumi- 
nation. The  emitted  radiation  is  very  complicated  and  depends  upon 
the  wave-length  of  the  exciting  source.  The  stimulus  may  have  an 
entirely  different  wave-length  from  any  line  in  the  emission  spectrum 
of  the  pure  vapor.  As  briefly  described  in  the  latter  part  of  this  chapter, 
fluorescence  may  be  generally  ascribed  to  unstable,  polyatomic,  molecu- 
lar formations. 


LINE  ABSORPTION  SPECTRA  91 

THE  BROADENING  OF  SPECTRAL  LINES 

We  have  seen  that  the  narrow  portion  of  the  line  X  2537,  represented 
by  the  resonance  radiation  from  mercury  vapor  at  room  temperature, 
is  almost  totally  absorbed  by  a  very  short  column  of  mercury  vapor  at 
0.001  mm  pressure,  while  by  increasing  the  pressure  to  several  mm  the 
entire  line  is  absorbed.  On  further  increase  in  pressure  the  line  widens 
into  a  band. 

The  increase  in  width  of  an  absorption,  or  emission,  line  has  been 
considered  from  the  classical  dynamical  standpoint  by  Rayleigh,24 
Lorentz25  and  others.  Rayleigh  discusses  five  different  causes  for 
broadening,  and  Franck26  has  interpreted  three  of  these  in  relation  to 
the  quantum  theory.  Two  causes,  the  Doppler  Effect  and  Impact 
Damping,  are  of  particular  interest. 

Doppler  Effect.  From  the  classical  theory,  a  quasi-elastically  bound 
electron,  vibrating  with  a  frequency  VQ  and  moving  with  a  velocity  v 
in  a  direction  making  an  angle  <j>  with  the  line  drawn  from  the  atom  to 
the  observer  gives  rise  to  the  frequency 


v  =  v0    l  +  -cos<f> 


where  c  is  the  velocity  of  light.  In  consequence  of  the  Maxwellian 
distribution  of  velocities  of  the  atoms  of  a  radiating  gas,  we  have  a 
broadening  of  the  spectral  line  about  the  monochromatic  frequency  VQ, 
which  leads  directly  to  the  useful  expression  given  on  page  27  for  the 
width  of  a  line.  In  general  v  is  small  compared  to  c,  so  that  the  broaden- 
ing amounts  to  only  a  few  hundredths  of  an  Angstrom.  In  the  case  of 
canal  rays,  however,  we  have  a  stream  of  radiating  atoms  projected  with 
high  velocity  in  a  single  direction,  so  that  instead  of  a  broadening  we 

have  a  shift  of  frequency  Aj7  =  =F  VQ  - ,  according  as  one  looks  with  or 

c 

against  the  direction  of  propagation  of  the  beam,  amounting  to  an 
easily  observable  quantity,  of  the  order  of  an  Angstrom  unit. 

The  above  explanation,  which  is  so  simple  from  the  classical  dynamical 
standpoint,  especially  in  its  relation  to  familiar  acoustical  phenomena, 
is  by  no  means  satisfactory  on  the  basis  of  the  quantum  theory.  Here 
we  give  individuality  to  the  quantum  and  are  led  to  question  how  the 
energy  of  a  quantum  projected  in  the  direction  of  the  beam  may  differ 

2<  Phil.  Mag.,  29,  pp.  274-84  (1915). 
»  K.  Akad.  Amsterdam  Proc.,  18,  pp.  134-50  (1915). 

»•  "The  Broadening  of  Spectral  Lines,"  5  pp.,  Anniversary  Volume  of  Kais.  Wilh.  Ges. 
(1921). 


92  ORIGIN  OF   SPECTRA 

by  2  Mi*  ergs  from  that  projected  at  180°  to  this  direction.  The  ex- 
planation lies  in  the  effect  of  the  radiation  pressure.  The  emission  of  a 
quantum  projected  in  the  direction  of  the  speeding  atom  produces  a 
recoil  upon  the  atom  and  retards  it.  The  quantum  thereby  abstracts 
from  the  kinetic  energy  of  the  atom,  hkv  ergs,  so  that  the  frequency  of 
emission  is  increased  by  Ay.  If  the  emission  takes  place  in  a  direction 
opposite  to  that  along  which  the  atom  is  projected,  the  atom  is  acceler- 
ated by  the  emission,  its  kinetic  energy  is  increased  by  Mj7  ergs,  and 
the  frequency  of  the  quantum  is  lowered  by  Ai/. 

The  magnitude  of  the  Doppler  effect  thus  remains  the  same,  but 
the  interpretation  of  the  phenomenon  is  different  by  the  two  theories. 

Impact  Damping.  At  high  pressure  and  also  in  a  strong  electrical 
discharge  the  broadening  of  lines  may  be  many  times  greater  than  that 
attributable  to  the  Doppler  effect.  Lorentz  considered  this  phenomenon 
as  due  to  impacts  from  neighboring  atoms  which  an  atom  suffers  during 
the  process  of  emission.  If  the  emission  is  broken  up  by  the  impact, 
or  if  a  phase  change  is  produced,  it  may  be  shown  that  the  emitted 
radiation  will  consist  of  a  dispersion  of  frequencies  which  is  greater 
the  shorter  the  time  of  the  undisturbed  emission.  Since  the  number  of 
impacts  increases  with  increasing  pressure,  we  obtain  an  increase  in 
broadening  of  the  line,  a  fact  well  established  by  experiment. 

The  quantum  theory  substitutes  for  impact  damping  the  influence 
of  the  electrical  fields  of  neighboring  atoms  upon  the  position  and  energy 
of  the  electron  in  a  quantized  orbit.  Since  the  energy  of  any  orbit  is 
altered,  the  energy  difference  of  the  two  orbits  between  which  an  electron 
jump  takes  place  may  be  changed,  with  a  resulting  modification  of  hv. 

As  will  appear  in  the  following  section,  an  electron  may  occupy  an 
outer  orbit  in  an  undisturbed  atom  for  an  appreciable  length  of  time  r. 
Franck  believes  that  if  such  an  atom  which  is  in  a  condition  to  emit  a 
spectral  line,  collides  with  another  atom,  the  time  r  is  immediately 
altered  and  the  emission  is  forced  to  take  place  while  the  orbits  of  the 
radiating  atom  are  deformed  by  the  electrical  field  of  the  impacting 
atom.  Since  all  types  of  collision  may  occur,  resulting  in  different  de- 
grees of  orbital  deformation,  a  dispersion  of  frequencies  will  be  produced 
with  a  resulting  broadening  of  the  emission  line.  Also  since  the  number 
of  collisions  increases  as  the  pressure  is  raised,  the  amount  of  broadening 
should  increase.  An  analogous  interpretation  may  be  given  to  the 
phenomenon  of  absorption  so  that  probably  the  remarkable  broadening 
of  the  absorption  lines  noted  in  the  foregoing  section  is  mainly  due  to 
the  disturbance  of  inter-atomic  fields  by  atomic  collision. 


LINE  ABSORPTION  SPECTRA  93 

LINE  ABSORPTION  SPECTRA  OF  EXCITED  ATOMS 

An  excited  atom  is  one  having  an  outer  electron  in  an  orbit  other 
than  its  normal  orbit.  We  shall  first  consider  atoms  for  which  the 
outer  electron  is  in  the  orbit  of  next  higher  energy  level  than  that  of  the 
normal  position.  For  hydrogen  this  is  the  second  ring;  for  the  alkalis, 
the  orbit  2  pi  or  2  p2;  and  for  the  metals  of  Group  II  of  the  periodic 
table,  the  orbit  2  p2.  In  the  latter  case  we  shall  neglect  consideration 
for  the  present  of  the  orbit  2  p3  which  lies  between  1  S  and  2  p2. 

Two  means  have  been  already  discussed  by  which  the  valence  electron 
may  be  ejected  to  this  second  orbit.  First,  as  the  immediate  result  of 
an  electron  collision  at  the  resonance  potential  or  as  an  indirect  result  of 
recombination,  following  ionization,  and  return  toward  normal,  the 
electron  may  temporarily  assume  a  position  in  the  second  orbit.  Second, 
the  electron  may  be  ejected  to  the  second  orbit  directly  by  absorption 
of  radiation  of  such  frequency  as  Is  —  2  p  or  1  $  —  2  p2  as  discussed 
in  the  preceding  section,  or  indirectly  by  the  absorption  of  any  radi- 
ation of  the  type  Is  —  mp  followed  by  subsequent  emission  of  a  line 
in  a  series  converging  at  2  p.  A  third  method,  which  is  discussed  in 
Chapter  VII,  involves  a  consideration  of  the  effect  of  elevated  temper- 
atures. There  is  evidence  that  merely  heating  a  gas  drives  a  valence 
electron  to  an  outer  orbit. 

The  electron  once  in  the  second  orbit  does  not  in  general  remain 
there  long,  and  if  undisturbed  falls  into  the  normal  orbit  emitting  the 
first  line  of  the  principal  series  —  the  single-line  spectrum  —  as  shown 
in  Chapter^.  The  question  as  to  the  length  of  time  r  the  second  orbit 
is  occupied  is  a  most  fundamentally  important  one  and  will  be  considered 
below. 

THE  MEASUREMENT  OF  T 

Suppose  in  the  case  of  mercury  that  the  atom  remains  in  the  excited 
condition  for  exactly  r  sec.,  and  that  the  time  required  for  a  stimulus 
to  thus  activate  the  atom  and  the  time  during  which  radiation  is  subse- 
quently emitted  is  small  compared  to  r.  That  is,  suppose  the  time 
required  for  any  interorbital  transition  were  negligibly  small  compared 
to  the  time  during  which  an  electron  occupied  an  outer  ring  such  as  the 
2  p2  orbit.  This  being  true  we  shall  consider  what  may  be  done  with  a 
unidirectional  stream  of  mercury  vapor  issuing  from  a  properly  designed 
nozzle,  as  shown  in  Figure  16.  This  stream  is  illuminated  at  b  by  a 
small  diaphragmed  beam  of  radiation  of  wave-length  X  2537,  the  cross 


94 


ORIGIN  OF  SPECTRA 


section  of  the  beam  being  represented  by  c.  The  atoms  are  accordingly 
stimulated  at  b  and  for  each  excited  atom  a  valence  electron  is  ejected 
to  the  2  p2  orbit,  as  a  result  of  the  exciting  radiation.  On  account  of 
the  velocity  of  translation  of  the  atoms,  which  may  be  determined  by  a 
measurement  of  the  temperature  of  the  boiling  vapor  or  by  other  means, 
the  atoms  travel  to  the  position  b'  before  returning  to  the  normal  state. 
Accordingly  at  b'  there  should  be  an  emission  of  the  line  X  2537  and  the 
distance  b  to  b'  gives  a  measure  of  the  time  T  in  the  excited  state. 


FIG.  16.    Unidirectional  stream  of  mercury  vapor. 

Unfortunately,  although  such  an  experiment  yields  interesting 
results  which  will  be  considered  in  the  latter  part  of  this  chapter,  it  has 
no  bearing  upon  the  life  of  an  excited  atom.  That  this  is  true  is  evident 
from  a  consideration  of  the  molecular  velocities  involved.  The  most 
probable  velocity,  as  follows  from  the  kinetic  theory  of  gases,  is  given 
by  the  expression  v  =  12900  \/T/M  where  T  is  the  absolute  temperature 
and  M  the  molecular  weight  of  the  gas.  For  mercury  at  500°  abs  we 
obtain  a  velocity  of  2  X  104  cm/sec.  Hence  in  10-s  sec.,  which,  as 
will  appear,  is  the  probable  order  of  magnitude  of  the  result  desired, 


LINE  ABSORPTION  SPECTRA  95 

the  atoms  would  have  traveled  the  almost  imperceptible  distance 
2  X  10"^  cm.  Furthermore,  aside  from  the  above  and  the  question 
of  the  distribution  of  velocities  in  the  stream,  and  the  fact  that  the 
time  r  is  a  mean  phenomenon  analogous  to  mean  free  path,  etc.,  other 
difficulties  may  arise  which  make  such  an  experimental  arrangement 
impossible.  For  example  some  of  the  radiation  emitted  when  an  atom 
returns  to  the  normal  state  may  be  absorbed  by  a  neighboring  atom  so 
that  the  original  radiation  is  passed  on  successively  by  many  atoms,  if 
the  pressure  is  high,  before  it  finally  escapes  from  the  stream.  Horton 
and  Davies  observed  that  radiation  produced  at  the  resonance  potential, 
21.2  volts,  in  helium,  in  one  side  of  a  well-shielded  U-tube  was  passed 
on  from  atom  to  atom,  finally  appearing  at  the  other  end  of  the  tube. 
The  phenomenon  is  well  known  in  the  study  of  resonance  radiation 
where  the  entire  bulb  is  filled  with  a  glow  by  a  narrow  beam  of  exciting 
radiation.  If  this  effect  were  predominant,  measurements  such  as  the 
above  would  simply  give  the  average  length  of  time  that  the  radiation 
in  a  particular  apparatus  may  be  passed  on  from  atom  to  atom. 

We  define  r  as  the  average  time  during  which  an  electron  remains 
in  an  outer  orbit  of  an  atom.  If  at  a  given  time  t  =  0,  we  have  NO 
excited  atoms,  then  the  number  N  which  remain  in  the  excited  state 
after  t  seconds  have  elapsed  is 

N  =  NQe-2at,  - 
I 

!  where  a  is  a  constant.  It  is  at  once  apparent  that  the  average  value  of  t 
for  all  the  atoms  is  given  by  T  =  1/2  a. 

The  constant  a  may  be  determined  experimentally  in  the  following 
manner,  where  we  shall  consider,  for  simplicity  of  explanation,  the  X 
2537  line  of  mercury.  A  canal  ray  tube  is  employed  which  is  divided 
into  two  chambers,  A  and  B,  separated  by  the  cathode  through  which  an 
extremely  small  hole  or  slit  is  cut.  The  vapor  is  excited  in  chamber  A  by 
electronic  bombardment  at  several  thousand  volts.  The  resulting 
positive  ions  are  driven  to  the  cathode  and  some  of  these  are  projected 
with  high  velocity  through  the  hole  into  the  chamber  B.  This  latter  is 
maintained  at  the  highest  possible  vacuum  by  vapor  pumps,  liquid 
air,  etc.,  so  that  no  disturbing  collisions  will  occur  here.  The  cathode 
acts  a  shield  to  the  region  B,  keeping  away  stray  ejectrons.  Yet  it  is 
found  that  the  atoms  in  B  are  neutral.  This  means  that  each  atom 
projected  through  the  chamber  B,  as  the  result  of  the  velocity  which  it 
accumulated  while  an  ion  in  chamber  A,  recombined  somewhere  in  A, 
probably  very  close  to  the  cathode.  Let  us  assume  tentatively  that  at 


96  ORIGIN  OF  SPECTRA 


the  instant  each  now  neutral  atom  penetrates  chamber  B,  it  is  in  a  state 
to  emit  X  2537;  that  is,  a  valence  electron  lies  in  the  2  p2  orbit.  At 
this  point,  for  some  few  atoms,  the  valence  electron  drops  to  the  normal 
1  S  orbit,  the  process  occurring  for  all  the  atoms,  relative  to  time,  as 
indicated  by  the  above  equation.  Since,  however,  the  atoms  all  have 
a  very  high  unidirectional  velocity,  the  resumption  of  the  normal  condi- 
tion occurs  over  a  considerable  length  of  space  for  the  entire  group  of 
atoms.  As  each  return  to  normal  is  accompanied  by  the  emission  of  a 
quantum  of  X  2537,  we  obtain  a  streak  of  emitted  radiation,  which  may 
be  several  cm  in  length  for  a  light  element,  the  intensity  of  which  de- 
creases, as  follows  from  the  above,  proportionally  to  e~2ax/v,  where  x 
is  the  distance  of  penetration  in  B  and  v  is  the  velocity  of  the  stream. 
This  velocity  may  be  found  by  observation  of  the  Doppler  effect 
in  the  emitted  radiation.27 

Wien28  has  made  extensive  measurements  on  hydrogen,  nitrogen  and 
oxygen,  but  at  present  the  experimental  difficulties  have  not  permitted 
the  use  of  vapors  such  as  mercury.29  In  general  the  theory  is  not  quite 
as  simple  as  that  outlined  above.  The  atoms  entering  the  chamber  B 
are  in  excited  states  corresponding  to  the  outermost  quantized  orbits. 
They  are  therefore  capable  of  emitting  any  of  the  arc  lines.  The  inten- 
sity of  H0  (for  example)  representing  an  interorbital  transition  between 
orbits  of  quantum  numbers  4  and  2  first  increases  slightly  and  then 
decreases  in  accordance  with  the  law  already  given.  Mie3?  shows  such 
an  effect  is  to  be  expected. 

The  value  of  2  a  is  found  to  be  of  about  the  same  magnitude  for 
different  lines  even  with  different  elements.  For  the  0  and  7  lines 
of  hydrogen  Wien  observed  2  a  =  4.35  -107  sec"1  or  r  =  2.3  -10~8  sec. 
Dempster31  obtained  for  H0,  T  =  5- 10~8  sec. 

The  conception  of  the  occupancy  of  an  outer  orbit  for  an  appreciable 
time  has  as  an  analogue  the  emission  of  damped  vibrations  in  accordance 
with  the  ideas  of  classical  dynamics.  Thus  the  damping  constant  for  a 
radiating  electron  vibrating  about  its  position  of  equilibrium  may  be 
shown  to  have  the  form 

8 


3  me3 

"  Wood  has  described  several  methods  (Proc.  Roy.  Soc.,  99,  pp.  362-371,  1921)  for  the 
measurement  of  the  very  short  time  interval  between  the  absorption  of  light  by  phosphores- 
cent substances  and  its  re-emission.  Possibly  the  modification  of  the  Abraham  and  Lemoine 
method  therein  described  could  be  applied  to  the  measurement  of  T  for  resonance  radiation. 

28  Ann.  Physik,  60,  pp.  597-637  (1919);    66,  pp.  229-36  (1921). 

29  In  part  probably  because  of  the  very  high  voltage  necessary  to  produce  a  sufficient 
velocity  of  the  heavy  mercury  ions.    See  Fig.  45  (Appendix  I) . 

so  Ann.  Physik,  66,  pp.  237-60  (1921). 
si  Phys.  R.,  15,  pp.  138-9  (1920). 


96  A 


FIG.  17.  Spectrum  of  Zeta  Tauri  from  HT  to  limit  of  Balmer  series  (last  line  showing 
H3i)  made  with  37|  inch  reflector.  These  hydrogen  lines  are  all  absorption 
lines,  reversed  against  the  continuous  background  of  the  stellar  emission  spec- 
trum. 


FIG.  18.     Reversal  of  hydrogen  alpha  in  the  laboratory. 


J440 

j  1 1 1 1 1.  r. 


S+SO 


I 


S470 


iifii  iiTiiirhT 


I  III  I  ill  i  I  i  Til  1 1  I 


I 


I 


FIG.  19.  The  upper  spectrogram  shows  the  reversal  of  the  mercury  line  X  5461, 
2  pi  —  1  s,  against  the  solar  spectrum.  The  lower  spectrogram  shows  the  solar 
source  alone. 


LINE  ABSORPTION  SPECTRA  97 

This  gives  for  the  average  duration  of  the  emission  r  =  1/2  a  =  2- 10~8 
sec.  for  Ha.    In  general  we  may  conclude  that  r  is  of  the  order  10~8  sec. 

ABSORPTION  OF  SUBORDINATE  SERIES  LINES 

It  is  readily  seen  by  referring  to  the  energy  diagrams,  Figures  4  to  9, 
that  an  atom  having  an  electron  in  the  second  or  2  p  ring  is  capable  of 
absorbing  any  radiation  belonging  to  spectral  series  which  converge  at 
this  energy  level.  The  process  is  identical  with  that  discussed  in  the 
preceding  section,  except  all  the  transitions  take  place  from  the  second 
instead  of  first  orbit.  This  is  the  explanation  of  the  appearance  of  the 
Balmer  series  of  hydrogen  as  absorption  lines  or  of  the  frequently  ob- 
served reversals  of  lines  of  the  subordinate  series  in  the  case  of  the 
alkalis  and  alkali  earths.  Figure  17  shows  the  spectrum  of  Zeta  Tauri 
in  which  lines  of  the  Balmer  series  from  Hy  to  H3i  appear  sharply  re- 
versed. This  illustration  is  from  a  photograph  made  by  Dr.  R.  H. 
Curtiss,  University  of  Michigan,  for  the  authors.  The  absorption  is 
produced  by  a  stratum  of  excited  hydrogen  atoms  against  the  continuous 
emission  spectrum  from  an  interior  laye'r  in  the  star.32  The  solar  spec- 
trum also  shows  as  Fraunhofer  lines  many  lines  belonging  to  subordinate 
series,  for  example  the  C  line  which  is  Ha.  The  literature  abounds 
with  examples  of  such  reversals  in  the  arc.  Meggers33  mentions  the 
reversal  of  X  8183,  X  8195,  2  p  -  3  d,  the  first  pair  of  the  1st  Subordinate 
series  of  sodium.  Many  similar  cases  are  to  be  found  in  Kayser's  tables. 
The  arc  reversals,  which  appear  as  narrow  black  lines  on  the  bright, 
wider  background  of  the  emission  spectra  are  readily  observed  visually 
in  a  cored  carbon  arc.  Usually  they  flash  on  for  only  a  few  seconds: 
it  is  very  difficult  to  obtain  more  than  a  momentary  appearance  of  a 
large  number  of  such  absorption  lines  at  the  same  time.  This  momen- 
tary character  is  due  to  the  constant  shifting  of  the  envelope  of  absorbing 
and  excited  vapor  immediately  surrounding:  the  arc. 

Spectroscopists  have  in  the  past  made  little  differentiation  between 
the  reversal  of  a  line  of  a  principal  series  and  a  line  of  a  subordinate 
series.  In  fact  the  principal  series  of  an  alkali  has  been  incorrectly 
called  its  Balmer  series  because  its  lines  are  all  easily  absorbed,  giving  a 
spectrum  resembling  the  Balmer  lines  in  the  spectra  of  certain  stars 
(compare  Figures  12,  13,  and  17).  The  physical  mechanisms,  however, 
producing  the  Fraunhofer  C  and  D  lines  are  entirely  different,  a  fact 
readily  recognized  when  one  attempts  to  show  in  the  laboratory  the 
Balmer  absorption  spectrum  of  hydrogen.  No  one  has  ever  produced  in 

32  See  Chapter  VII.  »»  Bur.  Standards  Sci.  Paper.  No.  312. 


98  ORIGIN  OF  SPECTRA 

the  laboratory  a  subordinate  series  spectrum  at  all  resembling  that  given 
in  Figure  17,  although  it  is  not  difficult  to  obtain  such  a  spectrum  for  a 
principal  series. 

The  authors  have  devised  many  methods  for  producing  this  peculiar 
type  of  absorption  —  so  far  without  much  success.  The  resonance 
potential  of  the  hydrogen  atom  is  10.2  volts.  Hence  if  a  hydrogen 
atom  collides  with  a  10.2  volt  electron,  it  is  capable  for  an  instant  of 
absorbing  a  line  of  the  Balmer  series.  A  similar  condition  in  reference 
to  the  subordinate  series  holds  for  sodium  bombarded  by  2.1  volt  elec- 
trons. Another  suggested  method  is  to  illuminate  sodium  vapor  with 
intense  radiation  from  a  sodium  flame.  The  resulting  absorption  of  the 
D-lines  should  activate  the  sodium  atoms  so  that  they  would  be  capable 
of  absorbing  the  subordinate  series.  A  long  train  of  sodium  flames 
should  be  capable  of  showing  this  absorption.  Zahn,34  from  photo- 
metric measurements  and  determinations  of  the  quantity  of  sodium 
present  in  a  flame,  has  computed  that  each  sodium  atom  emits  about 
2000  quanta  of  D-radiation  per  second.  If  the  time  during  which  the 
atom  remains  in  the  active  state  is'10"8  sec.,  an  atom  on  the  average, 
per  second,  has  an  electron  in  the  2  p  ring  for  2000  X  10~8  or  about  10~5 
sec.  In  other  words  at  any  instant  about  1  in  50,000  sodium  atoms 
is  capable  of  absorbing  subordinate  series  lines.  This  proportion 
should  be  sufficient  to  show  some  effect  in  a  long  train  of  flames. 

While  these  experiments  bearing  directly  upon  the  quantum  theory 
of  absorption  have  not  as  yet  yielded  satisfactory  results,  there  are  many 
indirect  indications  of  its  validity.  It  is  very  difficult  to  produce  a 
sufficiently  long  column  of  vapor  heavily  bombarded  by  low  speed 
electrons  at  the  resonance  potential.  However,  with  a  Geissler  tube,  and 
high  potential,  a  very  long  column  of  excited  vapor  may  be  obtained. 
The  objection  to  this  method  of  activation  is  that  the  atoms  are  emitting 
the  complete  spectrum  and  hence  electrons  are  to  be  found  in  every 
possible  orbit  instead  of  the  second  orbit  only.  Since,  however,  the 
first  fundamental  line  of  the  type  1  s  —  2  p  is  emitted  strongly,  the 
orbit  2  p  is  occupied  to  some  extent  and  absorption  of  the  subordinate 
series  should  occur.  In  general  the  absorption  of,  for  example,  2  p 
—  3  d>  is  obscured  by  the  emission  of  this  line  by  the  gas.  but  there  are 
methods  for  detecting  it. 

Wood35  has  described  a  very  simple  method  for  observing  the  absorp- 
tion of  the  Balmer  line  Ha  in  hydrogen.  Using  a  lone-  discharge  tube 
arranged  for  end-on  observation  it  is  noticed  that  the  color  of  the  dis- 

*«  Verh.  d.  Physik.  Ges.,  15,  pp.  1203-14  (1913).  »  "Physical  Optics,"  2d  Ed. 


LINE  ABSORPTION  SPECTRA  99 

charge  is  rose-red  as  viewed  through  the  side  of  the  tube,  but  is  bluish- 
white  when  viewed  along  the  axis.  In  the  latter  case  the  red  line  has 
been  absorbed  by  the  long  column  of  excited  vapor.  A  similar  phenome- 
non may  be  observed  with  other  gases  and  vapors. 

Ladenburg36  has  obtained  a  reversal  of  H«  by  the  following  method. 
Two  long  discharge  tubes  are  mounted  on  a  common  axis  and  arranged 
with  windows  for  end-on  observation.37  These  are  excited  in  series 
by  an  induction  coil.  The  pressure  in  the  rear  tube  is  high  so  that 
broad  intense  emission  lines  are  produced.  The  vapor  in  the  front  tube 
both  emits  and  absorbs  H«,  but  by  proper  regulation  of  the  pressure  a 
narrow  reversal  may  be  obtained,  as  shown  by  Figure  18.  This  illustra- 
tion is  a  drawing,  as  the  actual  photographs  of  the  phenomenon,  though 
conclusive,  were  not  very  satisfactory  for  reproduction.  The  band  of 
light  is  the  broad  Ha  line  emitted  by  the  rear  tube  at  high  pressure. 
The  long  narrow  line  comes  from  the  front  tube.  A  small  portion 
of  this  is  reversed  where  it  crosses  the  emission  band  of  the  rear  tube. 
When  a  pulsating  discharge  is  used,  it  is  necessary  to  have  both  tubes 
glow  at  exactly  the  same  instant.  If,  however,  a  direct  current  dis- 
charge is  employed  for  the  absorption  tube,  a  continuous  source,  such 
as  an  electric  lamp,  may  be  used  for  the  background.  From  photometric 
measurements  upon  the  brightness  of  (1)  the  source  alone,  (2)  the  glowing 
absorption  tube  alone,  (3)  the  two  in  combination,  it  is  possible  to  com- 
pute the  absorption  coefficient  of  the  gas  for  the  various  spectral  lines. 
By  employing  high  dispersion  and  resolution,  Ladenburg  and  others 
have  determined  the  absorption  curve  over  the  single  line  H«,  and 
find  that  in  general  almost  complete  absorption  occurs.  None  of  the 
light  of  wave-length  Ha  from  the  background  penetrates  through  the 
excited  vapor. 

Metcalfe  and  Venkatesachar,38  using  a  tube  containing  mercury 
vapor  which  was  excited  by  a  small  current  above  the  ionization  po- 
tential, observed,  photometrically,  absorption  of  the  following  and 
other  mercury  lines. 


X 

Notation 

Remarks 

5461 

2Pl-ls 

strong 

4359 

2p2-  Is 

H 

4047 

2p3-ls 

11 

3342 

2pi  -  2s 

very  strong 

3663 

2  pi  -  3d 

strong 

36  Verb.  d.  Physik.  Ges.,  12,  pp.  54-80  (1910);   pp.  549-564  (1910). 

37  This  experiment  is  most  beautifully  made  by  use  of  discharge  tubes  with  windows 
fused  on  by  the  Fairchild  method,  cf.  J.  Optical  Soc.  Am.,  4,  p.  496  (1920). 

.  Roy.  Soc.,  100,  pp.  149-66  (1921). 


100 


ORIGIN  QF  SPECTRA 


They  state  that  the  absorption  of  X  2537, 1  S  —  2  p2,  is  not  increased 
when  the  vapor  is  luminous.  It  is  evident  that  such  should  be  the  case. 
If  any  perceptible  change  could  be  detected  the  luminous  vapor  should 
show  less  absorption  for  this  line  in  proportion  to  the  ratio  of  the  number 
of  excited  to  normal  atoms  —  actually  an  extremely  small  quantity. 
These  investigators  succeeded  in  obtaining  complete  reversal  of  the 
lines  2  pi  —  I  s  and  2  p2  —  1  s.  The  lower  spectrogram  of  Figure  19 
was  obtained  by  sighting  directly  on  the  sun  and  shows  the  Fraunhofer 
lines,  while  for  the  upper  spectrogram  a  column  of  excited  mercury  vapor 
was  interposed  in  the  line  of  sight.  The  reversal  of  the  green  mercury 
line  2  pi  —  I  s,  \  5461  A,  shows  clearly  in  the  upper  spectrogram. 

One  of  the  most  interesting  contributions  to  this  subject  has  been 
made  recently  by  Fuchtbauer.39  He  employed  a  double-walled,  long 
cylindrical  tube  of  quartz  between  the  two  walls  of  which  a  mercury 
arc  was  excited.  In  the  central  open  space  coaxial  with  the  discharge 
tube  was  mounted  a  second  closed  quartz  tube  fitted  with  windows  for 
end-on  observation.  This  second  tube  contained  mercury  vapor  the 
pressure  of  which  could  be  regulated.  The  emission  tube  was  further 
jacketed  outside  with  a  layer  of  mercury  which  acted  as  a  reflector 
concentrating  the  radiation  on  the  interior,  and  the  entire  system  was 
cooled  by  an  ice  bath.  When  the  vapor  pressure  in  the  inner  tube  was 
adjusted  to  that  corresponding  to  about  35°  C,this  vapor  became  in- 
tensely luminous,  emitting  all  the  arc  lines  of  mercury,  although  it  had 
no  connection  whatever  with  an  exciting  potential. 

This  fact  is  precisely  what  one  should  expect  on  the  basis  of  the 
quantum  theory  of  spectroscopy.  We  shall  analyze  these  results  in 
detail.  The  atoms  in  the  inner  tube  are  first  excited  by  radiation  of 
some  frequency  belonging  to  a  series  converging  at  1  S.  There  are  two 
such  series  1  S  —  mP  and  1  S  —  mp2.  According  to  the  theory  an 
electron  would  be  ejected  to  an  mP  or  an  mpz  orbit  by  absorption  of  the 
corresponding  spectral  line  in  these  two  series.  The  first  line  of  the 
first  series  is  X  1849.  The  first  two  lines  of  the  second  series  are  X  2537 
and  X  1292.  The  radiation  from  the  enveloping  quartz  lamp  must  pass 
through  two  quartz  walls  before  it  reaches  the  vapor  in  the  inner  tube. 
Fused  quartz  is  opaque  to  all  lines  of  these  series  except  X  2537  and  to 
some  extent  X  1849.  Fuchtbauer  states  that  practically  no  light  of 
wave-length  X  1849  was  transmitted.  Certainly  the  radiation  of  this 
wave-length  would  be  weak  compared  to  X  2537  and  we  shall  omit  its 
consideration.  In  so  doing,  however,  the  bearing  of  the  theory  upon 

39  Physik.  Z.,  21,  pp.  635-8  (1920). 


LINE  ABSORPTION  SPECTRA 


101 


the  observed  phenomenon  is  unaltered.     A  similar  analysis  may  be 
carried  through  by  the  reader,  admitting  the  presence  of  X  1849. 


FIG.  20.     Small  portion  of  energy  level  diagram  for  mercury. 

Accordingly  the  radiation  chiefly  effective  in  initially  exciting  the 
vapor  is  1  S  -  2  p2,  \  2537.  This  radiation  is  absorbed  by  the  vapor 
and  each  excited  atom  has  an  electron  in  the  2  p2  orbit.  Before  the 
electron  has  time  to  return  to  the  1  S  orbit,  with  a  resulting  emission  of 
X  2537,  it  absorbs  a  quantum  of  energy  of  some  frequency  belonging  to  a 
series  converging  at  2  p2.  This  radiation  is  readily  transmitted  through 
the  quartz.  The  azimuthal  quantum  number  of  the  2  p2  orbit  is  2. 
Hence  since  there  is  no  disturbing  electrostatic  or  magnetic  field,  this 
absorption,  by  the  Bohr  principle  of  selection,  will  displace  the  electron 
to  an  orbit  where  the  azimuthal  quantum  number  is  either  1  or  3, 
that  is  to  a  ms,  mS,  md,  or  mD  orbit  of  higher  energy  level,  and  the  line 
absorbed  from  the  exciting  radiation  will  belong  to  one  of  the  four 
series  which  converge  at  2  p2.  The  process  is  illustrated  by  the  energy 
level  diagram,  Figure  20,  on  which  &few  of  these  transitions  are  indicated. 


102  *'0&IQlff'Of  SPECTRA 

Suppose  the  atom  absorbed  the  line  2  p2  -  3  dr,  X  3126.  The  electron 
is  accordingly  displaced  to  the  3  d'  orbit  and  the  atom  is  in  a  position 
to  absorb  lines  of  the  Bergmann  series.  This  process  may  be  continued 
with  a  multitude  of  variations  up  to  the  point  where  the  electron  is 
completely  removed  and  the  atom  is  ionized.  At  any  stage  in  the 
process  the  electron  if  undisturbed  may  return  to  normal  either  directly 
or  by  successive  steps,  emitting  various  lines  of  the  arc  spectrum,  some 
of  which  are  shown  by  dotted  lines  in  Figure  20.  If  the  atom  with  the 
electron  in  the  2  p2  orbit  absorbs  the  line  2  p2  —  Is, it  is  then  in  a  position 
to  emit  the  lines  2  pi  —  I  s  or  2  ps  —  1  s  and  the  electron  falls  to  the 

2  pi  or  2  p3  orbits  respectively.     These  two  configurations  possibly 
constitute  metastable  forms  of  the  mercury  atom  just  as  in  the  case  of 
helium,  where  we  found  that  the  orbits  2  S  and  2  s  represented  metastable 
forms  of  this  element.     Lines  of  the  wave  numbers  v  =  1  S  —  2  p\ 
and  1  S  —  2  p3  are  not  observed  in  the  arc  spectrum  of  mercury,  showing 
that  an  electron  in  either  the  2  p\  or  2  p3  orbit  may  reach  normal  only 
by  absorption  of  energy  and  hence  by  passing  through  an  orbit  corre- 
sponding to  a  greater  energy  level.     . 

If  the  atom  with  an  electron  in  the  2  p2  orbit  absorbs  the  line  2  p2  — 

3  d',  X  3126,  and  then  emits  the  line  2  P  -  3  d',  X  5770,  the  electron  is 
transferred  to  the  2  P  orbit.     It  is  now  in  a  position  to  emit  1  S  —  2  P, 
X  1849.    Also  transitions  are  readily  apparent  by  which  the  electron 
may  be  ejected  to  the  3  p2  orbit  where  it  is  in  a  position  to  emit  the  line 
1  S  —  3  p2,  X  1292.     Accordingly  by  this  simple  process  lines  of  very 
much  higher  frequencies  than  those  present  in  the  exciting  source  are 
easily  stimulated.    This  fact  alone  should  be  sufficient  argument  for 
discarding  Stokes'  law40  which  now  has  as  many  exceptions  as  verifica- 
tions, and  is  of  little  value,  although  often  quoted.     It  should  be  noted 
that  the  production  of  radiation  by  the  absorption  of  radiation  of  lower 
frequency  is  in  accord  with  the  principle  of  conservation  of  energy.     In 
the  above  example  we  have  several  frequencies  transformed  into  one 
of  higher  value,  subject  to  the  energy  relation  2fc/i^  =  chv  =  energy, 
where  v>vt. 

The  entire  experiment  just  discussed  depends  upon  the  absorption 
of  the  fundamental  line  1  S  —  2  p2,  X  2537.  When  this  line  was  cut 
off  by  a  thin  cylinder  of  glass,  no  effect  whatever  could  be  detected. 
The  glass  transmits  freely  the  lines  of  series  converging  at  2  p2)  but  since 
with  the  glass,  there  is  no  radiation  transmitted,  through  the  absorption 

40  This  law  states  that  the  emitted  radiation  can  not  have  a  shorter  wave-length  than 
that  of  the  stimulus. 


LINE  ABSORPTION  SPECTRA  103 


of  which  the  electron  can  reach  the  2  p2  orbit,  the  vapor  in  the  inner 
tube  is  unaffected. 

We  have  already  pointed  out  that  with  helium,  when  an  electron 
is  displaced  from  its  normal  orbit  it  tends  to  assume  either  the  2  S  or 
2  s  orbits,  which  are  the  basic  energy  levels  for  the  two  systems  of  spectral 
series  for  this  element.  Apparently  these  orbits  may  be  occupied  for  a 
much  greater  length  of  time  than  10" 8  seconds.41  Hence  lines  in  series 
converging  at  either  2  S  or  2  s  should  readily  show  absorption,  as  is 
apparent  from  Figure  10.  Paschen42  has  observed  absorption  of  the 
lines  2  S  -  2  P,  X  20582,  and  2  s  -  2  p,  X  10830,  in  a  Geissler  tube 
excited  by  a  weak  current.  The  stimulating  current  causes  ionization 
of  the  gas  which  is  followed  by  recombination.  The  electron  returns 
toward  normal  by  successive  interorbital  transitions,  with  resulting 
radiation,  ultimately  reaching  the  orbits  2  S  or  2  s,  which  are  occupied 
for  an  appreciable  time.  In  this  state  the  two  most  prominent  absorp- 
tion lines  should  be  those  observed  by  Paschen.  The  effect  is  of  course 
assisted  by  any  electronic  impact  at  the  resonance  potential  in 
which  case  an  electron  may  be  ejected  directly  to  the  2  S  or  2s 
orbits. 

A  simply  ionized  atom  should  be  capable  of  absorbing  lines  of  the 
enhanced  spectrum.  The  ionized  alkali  earths  should  readily  show 
absorption  for  the  pair  1  @  —  2  $1)2,  and  for  higher  terms  in  this  series. 
No  laboratory  experiments  have  been  performed  to  test  this  fact,  but 
scattered  observations  point  to  its  truth.  King43  finds  that  both  mem- 
bers of  this  doublet  for  calcium,  X  3968  and  X  3933,  may  appear  reversed 
in  furnace  spectra.  These  lines  are  respectively  the  H  and  K  Fraun- 
hofer  absorption  lines  in  the  solar  spectrum.  The  corresponding  pairs 
for  strontium  and  barium  also  appear  as  absorption  lines  in  the 
sun.  The  pair  is  reversed  in  the  spark  spectra  of  Mg,  Ca,  Sr. 
and  Ba. 

We  may  have  excited  ionized  atoms  which  behave  precisely  like 
the  excited  un-ionized  atoms  discussed  in  the  foregoing  paragraphs. 
With  certain  types  of  excitation  the  remaining  valence  electron  for 
the  atoms  of  metals  of  Group  II  may  be  ejected  to  an  outer  orbit  such  as 
2  ^3,  under  which  condition  the  atom  absorbs  lines  of  the  enhanced  sub- 
ordinate series.  The  following  partial  list  of  reversals  of  enhanced 
lines  of  subordinate  series  is  typical.44 

41  See  pages  73  and  93. 
"Ann.  Physik,  45,  pp.  625-56  (1914). 
«  Astrophys.  J.,  51,  pp.  13-22  (1920). 

44  Compiled  mainly  from  Kayser's  tables.  These  reversals  are,  however,  a  matter  of 
common  experience. 


104 


ORIGIN  OF  SPECTRA 
TABLE  XVIII 


Element 

Notation 

X 

Source 

Mg 

2$!  -  35) 

2798 

Spark 

2  <p2  _  3  £> 

2790 

it 

2  ^2  -  2  3 

2928 

il 

Ca      

2$!  -  2(3 

3737 

u 

2  sp2  —  2  <3 

3706 

« 

2$i  —  3  $>2 

8498 

Sun 

2?i-  3S>i 

8542 

" 

2  $2  —  3  $)2 

8662 

tt 

2  $!  —  4  £)2 

3181 

Spark 

2?i  -  4®! 

3179 

u 

Sr 

2$!  -  2(3 

4305 

u 

2  $2  -  2  (3 

4161 

11 

2  ^!  —  4$)2 

3475 

(I 

2?i  -4S>i 

3464 

(I 

Ba  

2  ^i  —  2  (5 

4525 

u 

2^-4®2 

4166 

(I 

2  ''Pj  —  4  2)i 

4130 

(( 

2  $2  —  4  $)2 

3891 

u 

2  ^5j  _  5  ^j 

2634 

(I 

2  ^p2  _  5  $)2 

2528 

u 

Reversals  of  enhanced  lines  are  of  particular  interest  in  celestial  spec- 
troscopy,  where  they  furnish  an  indication  of  stellar  temperatures  as 
indicated  in  the  latter  part  of  Chapter  VII. 

We  shall  consider  briefly  some  of  the  rather  speculative  deductions 
to  be  drawn  from  experiments  with  a  stream  of  mercury  vapor.  Phillips45 
employed  a  long  inverted  quartz  U-tube;  closed  at  each  end.  The  leg 
containing  mercury  was  heated  to  350°  C,  while  the  other  leg  into  which 
the  mercury  distilled  was  water  cooled.  Just  above  the  surface  of  the 
boiling  mercury  a  beam  of  radiation  of  wave-length  X  2537  was  pro- 
jected through  the  vapor.  The  entire  tube  was  immediately  filled 
with  luminous  radiation.  Figure  21  shows  a  spectrogram  of  the  fluores- 
cent light.  The  resonance  line  X  2537  is  predominant,  and  in  addition 
we  have  a  band  of  radiation  in  the  extreme  violet  and  another  band, 
which  accounts  for  the  visible  luminosity,  in  the  green.  The  faint  lines 

«  Proc.  Roy.  Soc.,  89,  pp.  39-44  (1913). 


LINE  ABSORPTION  SPECTRA  105 

on  the  right  are  due  to  stray  radiation  from  the  source.  Wood46  by  a 
very  ingenious  method  found  that  the  luminosity  began  to  appear 
about  1/16000  second  after  the  exciting  stimulus  was  applied.  At 
very  high  pressure  the  time  could  be  reduced  to  1/40000  second.  The 
fact  that  the  time  is  so  much  greater  than  10~8  second  suggests,  and  the 
appearance  of  a  band  spectrum  shows,  we  are  dealing  with  a  new  phe- 
nomenon. Franck  and  Grotrian47  have  repeated  these  experiments, 
with  various  modifications,  from  which  they  have  drawn  conclusions 
which  will  be  reviewed  in  the  following  paragraphs. 

In  general  band  spectra  are  attributed  to  molecules.  Excited  atoms 
possess  an  electron  affinity  which  enables  them  to  unite  with  other 
atoms  forming  compound  molecules.  The  subject  of  electron  affinity 
is  briefly  considered  in  Chapter  VIII.  We  may  here  state  that  an  atom 
possessing  an  electron  affinity  may  attract  an  electron  and  become  a 
negative  ion.  Work  must  be  done  upon  the  negative  ion  to  reduce  it  to  a 
normal  atom.  Metals  and  the  rare  gases  in  their  normal  states  do  not 
possess  an  electron  affinity.  We  shall  first  consider  the  excited  helium 
atom  for  which  we  assume  that  there  is  one  electron  in  orbit  of  quantum 
number  1  and  one  electron  in  orbit  of  quantum  number  2,  the  orbits 
being  coplanar.  The  total  energy  of  this  configuration,  obtained  by 
means  of  Equations  (50)  and  (51)  is  as  follows: 

W  =  WP  +  Wa  =  -  4  Nhc  -0.25  Nhc  =  -  4.25  Nhc.  (71) 

The  helium  negative  ion  may  be  assumed  to  contain  one  electron  in 
orbit  of  quantum  number  1  and  two  electrons  in  orbit  of  quantum 
number  2.  Whence  by  means  of  the  same  equations  we  find: 

W '  =  W'v  +  W'q  =  -  4  Nhc  -  0.28  Nhc  =  -  4.28  Nhc.         (72) 

The  second  state  is  accordingly  stable.  Work  has  to  be  done  upon 
the  helium  ion  thus  formed  to  remove  the  extra  electron.  This  work 
amounts  to  0.03  Nhc  ergs  or  0.4  volts. 

We  have  noted  the  extreme  stability  of  a  pair  of  electrons  grouped 
about  a  single  point  charge  nucleus.  The  normal  helium  structure  is 
characteristic  of  the  X-ring  of  all  the  elements.  This  tendency  to 
grouping  in  pairs  appears  now  in  the  formation  of  negative  ions,  but 
the  stability  of  such  an  outer  structure  built  about  not  only  a  nuclear 
charge  but  other  electrons  is  not  very  great.  We  have  in  these  negative 
ions,  formed  from  excited  atoms,  a  metastable  compound  of  an  atom 

"Proc.  Roy.  Soc.,  99,  pp.  362-71  (1921). 
*f  Z.  Physik,  4,  pp.  89-99  (1921). 


106  ORIGIN  OF  SPECTRA 

and  an  electron,  with  an  outer  structure  resembling  normal  helium,48 
and  an  electron  defect  in  the  next  to  the  outer  shell  which  normally 
is  the  outer  shell. 

If  an  excited  helium  atom  which  has  not  picked  up  an  extra  electron 
collides  with  a  similar  atom,  the  electron  affinity  of  each  atom  causes 
an  attraction  resulting  in  the  formation  of  He2.  Lenz49  has  already 
attributed  the  excitation  of  a  band  spectrum  of  helium  in  a  strong 
discharge  to  the  presence  of  the  helium  molecule. 

There  is  no  tendency  for  a  normal  argon  atom  to  become  negatively 
charged.  However,  in  the  Moore  tube  light,  the  pressure  at  the  anode 
may  be  double  that  at  the  cathode  (measurable  with  an  ordinary  mer- 
cury manometer)  on  account  of  the  drift  of  negatively  charged  argon 
atoms.  The  argon  atom  is  excited  and  an  electron  is  driven  to  the 
second  orbit.  In  this  condition  it  attracts  another  electron,  forming  a 
metastable  configuration  with  a  helium-like  outer  structure  and  an 
electron  defect  in  what  was  normally  the  outer  shell,  the  whole  being  a 
negative  ion. 

Franck  and  Grotrian  suggest,  that  in  a  manner  similar  to  the  for- 
mation of  negatively  charged  atoms  of  rare  gases,  negatively  charged 
atoms  of  metals  may  be  produced.  The  valence  electron  of  a  sodium 
atom,  for  example,  may  be  ejected  to  the  2  p2  orbit,  where  the  atom  as  a 
whole  may  possess  an  electron  affinity  and  may  become  a  negative  ion, 
while  there  is  no  tendency  to  such  a  condition  as  long  as  the  valence 
electron  remains  in  its  normal  orbit. 

The  mercury  stream  experiments  are  accordingly  interpreted  as 
follows.  The  radiation  of  wave-length  X  2537  is  absorbed  by  the  atom 
with  a  resulting  ejection  of  an  electron  to  the  2  pz  ring.  Ordinarily 
this  electron  would  return  to  normal  in  10~8  seconds  with  an  emission 
of  the  line  X  2537.  Practically  no  displacement  of  the  illuminated  spot 
would  be  detectable.  Franck  and  Grotrian  confirmed  this  fact  by 
employing  a  low  pressure  in  the  absence  of  any  foreign  gas.  At  higher 
pressures,  however,  the  short-lived  excited  mercury  atom  may  collide 
with  a  normal  mercury  atom,  forming  the  molecule  flg2.  The  excited 
atom  which  possesses  an  electron  affinity  is  the  negative  component  in 
this  compound.  It  has  in  the  union  a  helium-like  outer  shell,  completed 
by  a  valence  electron  of  the  normal  atom,  and  an  electron  defect  in  the 
next  to  the  outer  shell.  The  normal  atom  is  the  positive  constituent 
like  Na  in  NaCl.  This  new  molecule  possesses  a  temporary  stability 

48  Possibly  more  exact  considerations  would  make  the  resemblance  closer  in  that  the 
orbits  of  the  outer  pair  would  be  crossed,  as  illustrated  by  Figure  11. 
«  Verh.  Physik.  Ges.,  21,  p.  632  (1919). 


LINE  ABSORPTION  SPECTRA  107 

and  the  duration  of  the  after  glow  in  the  stream  is  a  measure  of  its  life. 
A  band  spectrum  results  from  the  movement  of  electrons  and  nuclei 
within  the  molecule.  Dissociation  arising  in  collision  either  with  normal 
•  mercury  atoms  or  foreign  gas,  permits  the  electron  in  the  excited  atom 
to  return  from  2  p2  to  the  1  S  orbit,  thus  emitting  X  2537,  as  shown  by 
Figure  21.  These  conclusions  have  been  fairly  definitely  verified  by 
several  experiments  which  cannot  be  discussed  here. 

The  foregoing,  while  it  apparently  explains  one  means  of  forming 
molecular  compounds,  is  not  the  complete  interpretation  of  the  experi- 
mental facts.  Sodium  vapor  at  fairly  high  density  shows  thousands 
of  fine  absorption  lines  which  Wood50  believes  are  the  complement  of 
the  fluorescent  spectrum  excited  by  white  light.  Light  may  be  ab- 
sorbed by  sodium  vapor,  from  a  nearly  monochromatic  source  in  which 
there  is  no  frequency  corresponding  to  any  line  of  the  principal  or  other 
series  of  sodium.  Hence  the  presence  of  the  absorbing  molecules  can- 
not be  attributed  to  the  preliminary  activation  of  the  atoms  by  the 
source  of  radiation.  Strong  monochromatic  illumination  of  sodium 
vapor  by  a  red  or  green  line,  not  present  in  the  arc  spectrum  of  sodium, 
.gives  re-emission  of  that  line  and  a  series  of  lines  at  intervals  of  about 
37  A  on  each  side  of  the  exciting  line.  These  spectra  are  almost  the 
exact  counterpart  of  the  phenomena  obtained  with  iodine.  The  theory 
that  they  likewise  are  due  to  a  diatomic  molecule  is  supported  by  this 
similarity,  but  the  presence  of  the  molecules  again  cannot  be  attributed 
to  activation  of  the  atoms  by  light  which  they  are  not  capable  of  absorb- 
ing. Likewise  with  mercury  fluorescence  it  is  found  that  the  most 
effective  illumination  is  not  light  near  X  2537  but  of  a  higher  frequency, 
again  in  no  relation  to  the  series  lines  of  the  mercury  atom.  We  accord- 
ingly see  that  molecular  compounds  may  be  formed  without  excitation 
of  the  atoms  by  light  of  a  series  converging  at  1  s  or  1  S.  It  appears 
necessary  to  assume  that  the  vapors  contain  molecular  formations 
whether  or  not  they  are  illuminated.  Wood  states  that  the  fluorescence 
of  mercury  appears  only  in  case  of  vapor  freshly  liberated  from  the 
fluid  metal.  Fluorescence  cannot  be  excited  in  a  bulb  of  cooling  (hence 
condensing)  mercury  vapor,  containing  an  excess  of  mercury  at  the 
same  temperature  at  which  it  is  brilliant  in  case  the  temperature  is 
rising,  accordingly  where  evaporation  is  taking  place.  Apparently 
then  molecular  compounds  such  as  Na2,  Hg2  may  be  evaporated  from 
the  liquid  surface.  Now  if  Franck  and  Grotrian's  explanation  of  the 
structure  of  these  compounds  is  correct,  that  is  if  Hg2  consists  of  an 

«  "Physical  Optics,"  2d  Ed. 


108  ORIGIN  OF  SPECTRA 

excited  and  a  normal  atom,  simply  boiling  mercury  briskly  should 
produce  an  emission  of  1  S  —  2  p2,  \  2537.  Decomposition  of  the 
metastable  compound  Hg2  should  release  an  atom  having  an  electron 
in  the  2  p%  ring  which  on  returning  to  normal  emits  this  fundamental 
line.  A  six  hour  exposure  to  a  vessel  of  boiling  mercury,  by  Dr.  Meggers 
and  the  authors,  failed  to  show  a  trace  of  this  line.  The  experiment, 
however,  is  worthy  of  further  thought. 

The  entire  subject  of  the  behavior  of  excited  atoms  is  a  new  field 
of  research  which  promises  interesting  development.  No  doubt  the 
chemist  of  the  future  will  deal  familiarly  with  such  compounds  as  the 
helides,  argides  and  so  on.51 

51  Since  this  book  has  been  in  press  a  note  by  A.  S.  King,  Proc.  Nat.  Acad.  Sci.,  8, 
pp.  123-5  (1922),  has  appeared,  in  which  he  makes  the  statement  that  the  subordinate  series 
of  Na,  K,  Rb,  and  Cs  have  been  reversed  in  furnace  spectra  obtained  by  heating  the  vapor  to 
a  high  temperature.  This  is  a  confirmation  of  the  theory  of  absorption  by  excited  atoms  where 
the  excited  atoms  are  produced  by  temperature,  i.e.  by  the  third  method  mentioned  at  the 
beginning  of  the  section  on  "Line  Absorption  Spectra  of  Excited  Atoms." 

A  very  important  paper  by  Franck  has  just  appeared,  Zeit.  Physik,  9,  pp.  259-66  (1922), 
on  the  subject  of  excited  atoms.  Klein  and  Rosseland  have  suggested  that  a  slow-moving 
electron,  in  collision  with  an  excited  atom,  may  gain  kinetic  energy  while  the  atom  is  assuming 
its  normal  state,  no  radiation  being  emitted  in  the  process.  This  is  the  converse  of  excitation 
by  collision.  Franck  has  extended  this  idea  to  coHisions  between  excited  and  unexcited  atoms, 
thereby  obtaining  a  partial  explanation  of  the  weakening  of  resonance*  radiation  by  the 
presence  of  foreign  gas.  The  theory  is  also  used  to  explain  the  appearance  of  Hg  \2537, 
1  S  -  2  pz,  when  Hg  vapor  is  excited  by  A  1849,  IS  -  2  P.  This  may  require  a  transition 
without  radiation  from  the  2  P  state  to  the  2  pz  state.  Cario,  working  in  Franck's  laboratory, 
has  shown  that  thallium  lines  appear  in  mixtures  of  Tl  and  Hg  vapors  excited  by  \  2537,  which 
is  interpreted  to  mean  that  excited  Hg  atoms  can  give  up  their  energy  to  unexcited  Tl  atoms 
with  which  they  collide.  Other  applications  are  to  the  sensitizing  of  photographic  plates  by 
staining,  to  the  bright  fluorescence  of  almost  all  substances  at  low  temperature,  and  to  the 
Maxwell  velocity  distribution  in  the  emission  of  electrons  from  heated  surfaces. 


Chapter  V 
Line  Emission  Spectra  of  Atoms 

We  have  seen  that  when  an  electron  in  an  atom  is  transferred  from 
an  outer  to  an  inner  orbit,  energy  is  released  as  a  quantum  of  radiation 
of  wave  number  v.  If  W  is  the  total  energy  of  the  atom  corresponding 
to  the  initial  configuration  and  W'  the  energy  of  the  final  configuration, 
the  wave  number  of  the  emitted  radiation  has  the  value : 

„=  (W  -  W')/kc. 

The  study  of  line  emission  is  accordingly  concerned  with  the  various 
modes  of  interorbital  transitions  of  electrons  which  result  in  a  decrease 
in  the  internal  atomic  energy.  Since,  however  the  normal  atom  in  the 
gaseous  state,  except  for  elements  having  an  electron  affinity  such  as 
the  halogens,  possesses  a  minimum  of  internal  energy,  it  is  first  necessary 
to  increase  this  energy  before  any  radiation  can  be  emitted.  This  is 
done  by  ejecting  an  electron  to  an  outer  orbit.  Spectroscopy  is  mainly 
concerned  with  the  interorbital  transitions  of  a  valence  or  outer  electron 
following  such  an  ejection. 

There  are  at  least  four  general  processes  through  which  an  atom 
may  be  left  in  a  condition  such  that  it  is  capable  of  emitting  line  spectra. 
A  valence  electron  in  an  atom  may  be  ejected  to  an  outer  orbit  (1)  by 
absorption  of  external  kinetic  energy  at  impact,  (2)  by  absorption  of 
radiation  as  discussed  in  the  preceding  chapter,  (3)  by  increase  in  tem- 
perature of  the  vapor  as  discussed  in  Chapter  VII.  (4)  The  valence 
electron  of  an  atom  in  a  molecular  compound  may  be  left  in  an  outer 
orbit  or  completely  removed  from  the  atom  in  the  process  of  dissociation 
of  the  molecule.  For  example,  as  shown  earlier,  the  molecule  Hg2  con- 
sists of  a  neutral  Hg  atom  and  a  Hg  atom  having  a  valence  electron  in 
the  2  pz  ring.  If  this  molecule  is  dissociated,  the  excited  atom  subse- 
quently should  emit  the  radiation  1  S  —  2  p2.  Hydrogen  iodide  upon 
dissociation  emits  the  hydrogen  spectrum  showing  that  in  this  molecule 
the  hydrogen  atom  possesses  greater  energy  than  in  its  normal  mon- 
atomic  state.  It  is  of  interest  to  note  that  it  requires  slightly  less  work 

109 


110  ORIGIN  OF  SPECTRA 

to  completely  remove  the  valence  electron  from  the  hydrogen  atom  by 
dissociation  of  HI  than  by  ionization  of  the  hydrogen  atom  directly.1 
Sodium  chloride,  dissociated  in  the  bunsen  flame,  emits  the  spectrum 
of  sodium,  to  some  extent  as  an  immediate  result  of  the  dissociation, 
indicating  that  in  the  molecule  the  sodium  atom  possesses  a  greater 
internal  energy  than  in  its  normal  vapor  state.  Spectroscopists  obtain 
the  spectra  of  various  metals  by  vaporization  and  dissociation  of  their 
salts  in  a  carbon  arc.  However,  it  may  not  necessarily  follow  that  the 
process  of  dissociation  leaves  the  atom  in  a  positively  ionized  state, 
even  though  the  complete  arc  spectrum  appears.  For  example,  the 
dissociation  of  CdMg  may  leave  one  of  the  atoms  as  a  negative  ion.2 
It  would  be  necessary  for  this  negative  ion  to  lose  two  electrons  before 
it  becomes  capable  of  emitting  all  lines  of  the  arc  spectrum.  Yet 
CdMg  in  an  arc  would  probably  show  the  spectra  of  both  metals.3  In 
this  and  similar  cases  the  dissociation  is  merely  a  method  for  obtaining, 
by  an  indirect  process,  vapor  of  the  metal  in  the  atomic  state  and  the 
emission  phenomena  properly  fall  under  the  classifications  (1).  (2),  and 
(3).  We  should  accordingly  distinguish  between  processes  of  dissoci- 
ation which  leave  the  atom  in  a  condition  to  immediately  emit  radiation 
and  those  where  the  dissociation  serves  merely  for  the  production  of  the 
metal  vapor.4 

Classification  (1)  broadly  interpreted  embraces  many  varieties 
of  energy  transfer.  Radiation  may  result  from  a  collision  of  an  atom 
with  an  alpha  particle,  with  a  heavy  ion,  possibly  with  a  neutral  atom 
or  molecule  if  the  speed  is  great,  but  especially  with  a  free  electron. 
Since  our  quantitative  knowledge  of  emission  is  almost  entirely  limited 
to  the  effect  of  collisions  between  atoms  and  electrons,  we  shall  confine 
this  section  to  a  consideration  of  these  phenomena.  The  relation  of 
the  processes  (2)  and  (3)  to  spectral  emission  are  treated  in  Chapters 
,VT  and  VII  respectively  and  will  be  only  casually  considered  for  the 
present.  The  fundamentally  important  factor  in  the  ordinary  produc- 
tion of  spectra  is  collision  between  electrons  and  atoms. 

We  have  seen  that  a  collision  between  an  electron  and  an  atom  of 
'the  rare  gases  or  metallic  elements  may  be  elastic,  but  at  certain  well- 
defined  velocities  of  the  impacting  electron  the  collision  is  inelastic.  As 

1  See  Table  XXXVIII. 

2  A  large  number  of  such  compounds  is  given  in  Gmelin- Kraut's  handbook.    Probably 
other  more  familiar  compounds  illustrating  this  point  occur  in  more  complex  molecules. 

3  Probably  any  alkali  hydride  would  show  both  the  spectrum  of  the  metal  and  the  atomic 
spectrum  of  hydrogen.    In  this  molecule,  however,  the  hydrogen  occurs  as  a  negative  ion. 

4  In  general  it  is  probably  true  that  even  hi  such  processes  as  the  injection  of  NaCl  hi 
the  arc,  the  salt  acts  mainly  as  a  carrier  for  the  sodium.    The  same  sodium  atom  once  dis- 
sociated from  the  naolecule  probably  loses  and  regains  its  valence  electron  many  times  before 
At  leaves  the  arc. 


LINE  EMISSION  SPECTRA  111 

discussed  in  Chapter  III  the  energy  lost  by  the  electron  and  absorbed 
by  the  atom  at  an  inelastic  collision  corresponds  to  either  a  resonance  or 
ionization  potential.  If  the  atom  is  ionized  by  the  collision,  the  ejected 
electron  may  return  to  its  normal  orbit  by  a  variety  of  interorbital 
transitions.  Each  transition  results  in  a  decrease  in  the  total  energy 
of  the  atom  and  is  accompanied  by  the  emission  of  one  quantum  of 
radiation.  The  various  possible  steps  or  energy  levels  for  several 
typical  cases  have  been  considered  in  the  discussion  of  Figures  4  to  6. 
If  the  electron  returns  from  without  the  atom  to  the  normal  state  in  a 
single  transition,  the  highest  convergence  frequency  in  the  spectrum  of 
the  neutral  atom  is  emitted.  The  wave  number  of  this  radiation  is 
determined  by  the  quantum  relation  hczv  =  eVflW,  where  7^  is  the 
jonization  potential  in  volts.  If  the  electron  returns  to  the  normal  state 
by  several  successive  transitions,  a  corresponding  number  of  quanta 
of  different  wave  numbers  are  emitted,  of  such  value  that  the  sum  of  the 
quanta  equals  the  total  energy  of  ionization,  thus : 

Zfccfyfc  =  eVi  •  108.  (73) 

With  numerous  atoms  and  electrons  returning  to  equilibrium  by  various 
paths,  we  have  as  the  composite  result  the  emission  of  the  complete 
spectrum  of  the  neutral  atom.  This  by  definition  is  known  as  the 
complete  arc  spectrum. 

The  energy  absorbed  by  the  atom  during  a  collision  of  the  resonance 
type  is  not  great  enough  to  ionize  the  atom  but  rather  is  just  sufficient 
to  displace  a  valence  electron  to  a  neighboring  orbit  of  higher  energy 
level.  Hence  the  atom  in  assuming  equilibrium  conditions  will  radiate 
this  energy  as  quanta  of  wave  number  v  such  that 

ZftcS  =  eVr  -  108,  (74) 

where  Vr  is  the  resonance  potential.  The  resulting  radiation  may 
be  termed  the  partial  arc  spectrum,  special  cases  of  which  are  the  so- 
called  single-line  spectrum  and  the  two-line  spectrum,  etc. 

The  foregoing  processes  which  concern  the  neutral  atom  may  also 
apply  to  an  atom  which  is  initially  simply  ionized.  If  an  ionized  atom 
collides  with  an  electron  of  sufficient  velocity,  the  collision  is  inelastic, 
the  atom  absorbing  the  kinetic  energy  of  the  impacting  electron.  If 
the  energy  absorbed  is  sufficient  to  completely  eject  another  valence 
or  outer  electron,  the  atom  is  doubly  ionized,  and  the  work  required  to 
eject  this  electron,  expressed  in  volts,  is  denoted  by  the  symbol  V* 
or  in  general  simply  V*.  Hence  Vt  gives  the  work  required  to  eject  the 
first  outer  electron  from  a  normal  atom,  and  F4*  the  work  required  to 


112  ORIGIN  OF  SPECTRA 

eject  the  second  electron  after  the  first  one  has  been  removed.  The 
second  electron  may  return  to  its  normal  state  by  a  variety  of  interorbital 
transitions.  Each  transition  results  in  a  decrease  in  the  total  energy 
of  the  simply  ionized  atom  and  is  accompanied  by  the  emission  of  one 
quantum  of  radiation.  An  example  of  the  different  energy  levels  in  a 
typical  case  (ionized  magnesium)  is  illustrated  by  Figure  7.  If  the 
electron  returns  from  without  the  atom  to  the  normal  state  in  a  single 
transition,  the  highest  convergence  frequency  in  the  spectrum  of  the 
simply  ionized  atom  is  emitted.  The  wave.  number  is  determined  by 
the  relation  hc2v  =  eV*  -  108.  If  the  electron  returns  to  the  normal  state 
by  several  successive  transitions,  a  corresponding  number  of  quanta  of 
different  wave  numbers  is  emitted  as  follows: 


=  eVt*  -  108.  (75) 

Hence  with  numerous  originally  doubly  ionized  atoms,  each  with  an 
outer  electron  returning  to  the  normal  state  of  the  simply  ionized  atom 
by  a  variety  of  interorbital  transitions,  we  have  as  the  composite  result* 
the  emission  of  the  complete  spectrum  of  the  simply  ionized  atom. 
This  by  definition  is  known  as  the  complete  spark  or  enhanced  spectrum 
(of  the  first  type). 

As  with  the  neutral  atom,  electronic  collisions  may  take  place  in 
which  the  energy  transfer  is  not  great  enough  to  remove  the  second 
electron  but  rather  is  just  sufficient  to  displace  it  to  an  outer  orbit. 
Hence  the  ionized  atom  in  assuming  equilibrium  conditions  may  radiate 
this  energy  as  quanta  of  wave  number  vt  such  that 

ZfccVt  =  e7r*.108,  (76) 

where  Vr*  is  the  resonar.ee  potential  for  the  simply  ionized  atom.  The 
resulting  radiation  may  be  termed  the  partial  enhanced  spectrum.  No 
direct  measurement!  of  VT*  have  been  made,  but  estimates  of  its.  magni- 
tude for  several  elements  may  be  obtained  from  spectroscopic  consider- 
ations, as  seen  later. 

The  numerical  relationships  in  the  foregoing  paragraphs  on  enhanced 
spectra  require  a  little  further  explanation  when  applied  to  metals  of 
Group  I  of  the  periodic  table,  since  for  these,  there  is  but  a  single  valence 
electron.  Removal  of  the  second  electron  accordingly  must  take  place 
from  what  is  normally  the  next  to  the  outer  shell,  as  will  be  considered 
later. 

We  note  that  a  simply  ionized  atom  may  emit  an  enhanced  spectrum 
of  the  "first  type."  The  above  process,  however,  may  be  repeated  so 
that  a  doubly  ionized  atom  should  emit  an  enhanced  spectrum  of  the 


112  A 


Ultra- violet 


Green 


EJ37  Sand  Band 

FIG.  21.     Fluorescent  radiation  from  mercury  vapor. 


c*    *  . 


. 


LINE  EMISSION  SPECTRA  113 

''second  type/'  etc.  Unfortunately  practically  nothing  is  known  from 
the  spectroscopic  standpoint  of  these  higher  types  of  spark  spectra 
and  we  shall  omit  their  further  consideration. 

Tt  is  noted  in  Chapter  III  that  the  magnitude  of  the  ionization 
potential  V  is  small  for  most  elements,  of  the  order  5  to  15  volts.  We 
shall  see  that  V*  also  is  not  great,  varying  from  10  to  50  volts  for  the 
elements  concerning  which  any  data  exist.  Hence  50  volt  electrons 
should  be  capable  of  exciting  the  enhanced  spectrum  of  nearly  every 
element.  It  has  been  found,  however,  that  the  spectrum  characteristic 
of  the  neutral  atom  predominates  in  the  arc,  whence  the  terminology 
"arc  spectrum."  For  the  excitation  of  the  enhanced  spectrum,  it 
usually  has  been  necessary  to  employ  a  very  high  potential,  thousands 
of  volts,  across  a  spark  discharge,  whence  the  terminology  "  spark 
spectrum." 

Accordingly  if  spark  spectra  should  appear  at  low  voltage  why  are 

they  absent  or  at  least  weak  in  the  cored  carbon  arc?     There  are  two 

reasons  for  this.     First,  it  is  difficult  to  maintain  much  of  a  field  in  a 

highly  ionized  space.    If  100  volts  is  applied  to  the  terminals  of  the 

arc,  as  soon  as  much  ionization  occurs,  the  actual  voltage  drop  in  the  arc 

falls  to  a  value  not  greatly  exceeding  the  ionization  potential,  and  the 

greater  portion  of  the  drop  is  shifted  to  the  leads.     This  is  simply  a 

i  consequence  of  Ohm's  law,  since  the  "  resistance"  of  the  arc  itself  ap- 

|  proaches  zero.     Secondly  and  more  important,  the  type  of  spectrum 

j  excited  has  little  immediate  relation  to  the  applied  voltage*but  instead 

I  depends  upon  the  speed  of  the  impacting  electron.     This  is  a  function 

of  the  voltage  drop  per  mean  free  path,  and  for  a  given  applied  voltage 

depends  upon  the  pressure. 

Suppose, « for  example,  we  had  two  large,  flat,  parallel  electrodes, 
separated  by  10  cm,  such  that  the  applied  field  produced  a  uniform 
potential  gradient  throughout  the  10  cm  length.  One  of  the  electrodes, 
e.g.  a  Wehnelt- cathode,  is  assumed  to  emit  electrons.  Let  us  suppose 
that  a  potential  difference  of  100  volts  is  maintained  across  these  ter- 
minals, and  the  space  is  filled  with  mercury  vapor  at  357°  C,  that  is, 
at  atmospheric  pressure.  We  find,  from  the  kinetic  theory,  for  the 
mean  free  path  of  an  electron,  to  an  approximation: 

mean  free  path  of  electron  =  I  =  l/irr^n  (77) 

where  r  is  the  radius  of  the  gas  atom  and  n  is  the  number  of  atoms  per 
cm3.  For  mercury  r  =  1.5  X  10~8  cm  and  in  the  present  example 
n  =  1.2-1019.  Hence  I  =  10~4  cm  and  the  voltage  drop  per  mean  free 
path  is  accordingly  0.001  volt.  The  lowest  resonance  potential  of 


114  ORIGIN  OF  SPECTRA 

mercury  is  4.9  volts,  and  electrons  having  an  energy  less  than  this  amount 
collide  with  the  atoms  elastically.  Accordingly  not  until  each  electron 
has  made  4900  collisions  has  it  accumulated  enough  kinetic  energy  to 
produce  any  disturbance  of  the  mercury  atom,  and  then  the  energy  is 
only  sufficient  to  displace  a  valence  electron  to  the  2  pz  ring.  (We  have 
neglected  in  this  simple  discussion  the  fact  that  the  direction  of  motion 
of  the  electron  is  altered  after  each  collision.)  It  is  evident  in  this 
extreme  example  that  very  few  electrons  will  ever  attain  10.3  volts 
velocity,  sufficient  to  ionize  mercury  and  produce  the  arc  spectrum,  to 
say  nothing  of  the  higher  velocity  required  to  excite  the  enhanced 
spectrum. 

By  fohe  time  the  electron  has  attained  4.9  volts  velocity  it  has  pro- 
gre  red  along  the  tube  a  distance  of  5  mm.  Here,  to  an  atom,  it  gives 
up  its  kinetic  energy,  which  is  subsequently  radiated  as  a  quantum  of 
wave  number  v  =  1  S  —  2  p2,  X  2537.  The  process  is  then  repeated, 
so  that  at  every  5  mm  along  the  tube  is  a  stratum  of  atoms  radiating 
this  ult "a- violet  line.  By  counting  the  striae  and  measuring  the  applied 
potential,  or  preferably  by  probe  wire  measurements  of  potential  at 
'  each^tria,  a  fairly  good  determination  of  the  resonance  potential  may 
Be  obtained.  The  following  illustrates  such  a  series  of  readings  made 
by  Grotrian.5 

Volts 15.2120.0    25.0129.6134.2    39.0    43.5  I  48.0  I  54.0    59.1    64.2169.0 

Difference...         4.8      5.0      4.6      4.6      4.8      4.5      4.5      6.0      5.1      5.1      5.2 

It  is  of  interest  that  although  the  light  radiated  by  the  mercury  atoms 
lies  in  the  ultra-violet,  there  is  present  the  green  fluorescence  characteris- 
tic of  the  molecules  formed  by  the  union  of  an  excited  and  normal  atom 
as  discussed  on  page  104.  Hence  the  striae  are  readily  visible  although 
no  ionization  is  present. 

The  fact  that  by  increasing  the  pressure  of  a  metal  vapor,  all  the 
energy  of  electronic  impact  can  be  forced  into  a  single  type  of  resonance 
collision  corresponding  to  the  lowest  resonance  potential,  is  frequently 
made  use  of  in  securing  a  large  number  of  reversals  in  the  partial  current 
curves6  even  at  voltages  far  exceeding  the  ionization  potential.  It  is  - 
also  well  known  that  by  employing  sodium  vapor  at  high  pressure 
very  efficient  "vacuum"  arc  may  be  obtained,  all  the  energy  of  electronic 
collision  going  into  the  production  of  the  D-lines,  the  first  pair  of  the 
principal  series.  The  same  phenomenon  is  of  course  true  physically 
for  any  vapor,  but  physiologically  sodium  stands  unique  in  the  close 

5  Z.  Physik,  5,  pp.  148-58  (1921). 

6  The  usual  method  for  determining  resonance  potentials.    See  references  to  Chapter  III. 


LINE  EMISSION  SPECTRA  115 


proximity  of  this  line  to  the  spectral  region  of  maximum  sensitivity  of 

P+,he  eye. 
The  foregoing  discussion  clearly  shows  why  spark  lines  are  not 
strongly  present  in  the  ordinary  two-electrode  arc.  Indeed  it  raises 
the  question  as  to  how  any  arc  lines  other  than  the  first  term  of  a  princi- 
pal series,  corresponding  to  the  lowest  resonance  potential,  may  be 
present.  We  may  cite  five  reasons  in  explanation  of  this. 

(1)  The  partial  pressure  of  the  metal  vapor  in  an  ordinary  cored 
carbon  arc  may  be  considerably  less  than  an  atmosphere  —  in  certain 
cases  possibly  only  a  few  mm  Hg.    The  lower  the  pressure  the  longer  is 
the  mean  free  path  and  hence  the  greater  is  the  chance  that  an  electron 
accumulates  velocity  sufficient  to  ionize.     Since  the  resonance  potentials 
of  the  atmospheric  gases  are  all  high,  collision  with  these  gas  moteules 
does  not  materially  affect  the  ability  of  the  electron  to  ionize  a  metal 
atom. 

(2)  The  phenomenon  of  absorption  of  radiation  is  undoubtedly 
a  controlling  factor  in  the  operation  of  many  arcs.    This  is  Discussed 
in  some  detail  in  Chapter  VI.     Collision  of  an  atom  and  a  free  electron^ 
at  the  resonance  potential  gives  rise  to  the  first  line  of  an  importan^    er ies, 
for  example  I  s  —  2  p  with  the  alkalis.     This  radiation  is  absorbed  by  a 
neighboring  atom  producing  an  ejection  of  an  electron  to  the  2  p  orbit. 
Before  the  excited  atom  can  resume  its  equilibrium  state  it  is  struck  by 

!  a  second  electron,  and  the  valence  electron  is  ejected  to  another  orbit 
:  of  still  higher  energy  level  or  may  be  completely  removed  from  the 
:  atom.  The  ordinary  mercury  vapor  arc  lamp  is  readily  operated  at  a 
pressure  greater  than  one  atmosphere  and  still  it  emits  the  complete 
arc  spectrum,  although  we  have  just  shown  that  many  thousands  of 
collisions  must  occur  before  the  electron  accumulates  the  velocity  cor- 
responding to  even  the  resonance  potential.  It  is  safe  to  conclude  that 
practically  no  electrons  at  this  vapor  pressure  have  a  velocity  much 
.greater  than  4.9  volts.7  However,  absorption  of  the  radiation  I  S  — 
2  p2  following  a  resonance  collision  leaves  the  atom  in  the  excited  state 
where  collision  with  an  electron  of  5.4  (  =  10.3  —  4.9)  volts  velocity  is 
sufficient  to  ionize.  The  ionizationlnay  be  the  result  of  several  absorp- 
tions of  radiation  followed  by  a  single  electronic  impact,  so  that  in 
general,  as  discussed  in  Chapter  VI,  ionization  may  take  place  in  an  arc 
in  which  there  are  no  electrons  having  a  velocity  greater  than  that 
corresponding  to  the  resonance  potential. 

7  A  few  electrons  very  close  to  the  anode  and  cathode  might  have  higher  velocities  for 
reason  (5). 


116  ORIGIN  OF  SPECTRA 

(3)  A  third  reason  why  the  complete  arc  spectrum  appears  in  a 
two-electrode  arc  is  the  phenomenon  of  successive  impact.     This  is  the 
same  in  principle  as  (2).     In  the  case  of  mercury,  for  example,  the  atom 
is  struck  by  a  4.9  volt  electron,  and  while  in  the  excited  state  a  second 
electron  collides  with  the  atom  and  raises  the  valence  electron  to  a  higher 
energy  level,  ultimately  producing  ionization. 

(4)  Although  the  mean  free  path  of  the  electron  may  be  too  small 
to  permit  the  accumulation  of  the  ionization  velocity  over  its  length,  a 
small  proportion  of  the  electrons  will  travel  many  mean  free  paths 
without  collision.     At  fairly  low  pressure  and  high  applied  voltage  this 
factor  may  attain  considerable  importance. 

(5)  The  production  of  any  ionization  alters  the  form  of  the  potential 
gradient  between  the  cathode  and  anode.     With  copious  ionization 
the  normally  negative  space  charge  around  the  cathode  may  be  neutral- 
ized, eventually  becoming  positive.    A  major  portion  of  the  potential 
drop  across  the  arc  may  then  occur  within  an  extremely  short  distance 
from  the  cathode.     Hence  the  emitted  electrons  have  an  opportunity 
for  accumulating  the  ionizing  velocity  during  a  mean  free  path.     Under 
other  circumstances  a  considerable  potential  drop  may  occur  at  the 
anode  with  a  similar  result.     Frequently  the  conditions  are  such  that 
the  total  potential  drop  is  divided  into  two  parts,  one  close  to  the  cathode 
and  the  other  close  to  the  anode,  with  little  continuous  potential  vari- 
ation through  the  arc  itself. 

From  the  above  considerations  it  is  evident  that  no  very  definite 
conclusions  can  be  drawn  experimentally  by  observing  the  voltage 
necessary  to  excite  particular  types  of  spectrum  in  a  two  electrode  arc. 
In  general  all  arc  lines  and  a  few  fundamental  spark  lines  appear  in  the 
arc  at  100  volts.  Enhanced  lines  are  readily  excited  in  a  spark  dis- 
charge at  several  thousand  volts.  Such  voltages  bear  no  relation  to  the 
minimum  energy  required  to  excite  these  spectra.  A  knowledge  of 
the  actual  velocity  of  the  electrons  at  the  instant  of  collision  with  (fcms 
is  necessary.  The  following  method  devised  by  the  authors  and 
Dr.  Meggers8  has  yielded  definite  and  conclusive  results. 

Three  electrodes  are  employed  arranged  as  shown  in  Figure  22. 
The  central  electrode  is  a  heated  cathode  of  tungsten,  molybdenum, 
lime-coated  platinum,  etc.,  depending  upon  the  nature  of  the  vapor. 
Around  this  js  mounted  as  closely  as  possible  a  spiral  grid,  arid  outside 
at  a  relatively  large  distance  is  placed  a  concentric  cylindrical  plate. 

s  Foote,  Meggerfe  and  Mohler,  PhU.  Mag.,  42,  pp.  1002-15  (1921) ;  Atrophys.  J.,  55, 
145-61  (1922);   Phil.  Mag.,  43,  pp.  659-61  (1922). 


LINE  EMISSION  SPECTRA 


117 


The  accelerating  field  for  the  electrons  is  applied  between  the  cathode 
and  grid,  the  latter  being  in  direct  metallic  contact  with  the  plate.  The 
pressure  of  the  vapor  is  so  regulated  that  relatively  few  collisions  of 
electrons  and  atoms  occur  in  the  short  space  over  which  the  accelerating 
field  is  applied.  Most  of  the  electrons  pass  through  the  grid  without 
collision,  thus  attaining  the  full  velocity  of  the  impressed  field.  These 
electrons  then  collide  with  atoms  in  the  large  force-free  space  between 
the  plate  and  grid,  giving  up  their  energy,  which  is  subsequently  radi- 


F/ELO 


Pia. 


a,  22.  Arrangement  of  electrodes  for  the  study  of  critical  voltages  required  to 
excite  different  types  of  spectrum.  The  grid  must  be  mounted  very  close  to  the 
cathode. 


ated  as  line  spectra.  By  observing  the  minimum  potentials  at  which 
the  different  types  of  spectrum  are  excited,  a  direct  determination  may 
be  made  of  the  amount  of  energy  necessary  for  their  production.  The 
values  so  obtained  in  all  cases  confirm  the  deductions  from  the  quantum 
theory.  It  is  of  interest  to  note  that  with  this  form  of  arc  the  higher 
series  terms  are  readily  photographed.  For  example,  the  authors  had 
no  trouble  in  observing  such  terms  as  p  =  2  p  —  IS  din  sodium,  rarely 
if  ever  detectable  in  an  ordinary  arc. 


118  ORIGIN  OF  SPECTRA 

We  shall  first  consider  the  metals  of  Group  II  of  the  periodic  table, 
then  the  alkalis  and  finally  some  observations  on  the  rare  gases.  It 
must  be  emphasized  that  the  attack  of  the  problem  from  our  present 
standpoint  is  new,  practically  all  work  being  done  during  the  past  year, 
and  hence  the  data  available  are  rather  meager  at  the  present  time. 

METALS  OF  GROUP  II  OF  THE  PERIODIC  TABLE 

These  metals  have  two  resonance  potentials.  We  should  accordingly 
expect  a  four  stage  development  in  the  spectra,  a  characteristic  spectrum 
at  the  lower  resonance  potential,  a  change  at  the  higher  resonance 
potential,  the  complete  arc  spectrum  at  the  ionizacion  potential  and 
the  complete  spark  spectrum  at  the  potential  necessary  to  remove  the 
second  valence  electron. 

As  discussed  on  page  39  the  spark  spectra  of  the  alkali  earths  re- 
semble the  arc  spectra  of  the  alkalis,  showing  series  of  doublets  as 
follows: 

Principal  v  =  1  @  -  w$i,2  m  =  2,  3,  4,  (78) 

1st  Subordinate  v  =  2  ^i,2  -  w®i,2  m  =  3,  4,  5,  .;  (79) 

2d  Subordinate  v  =  2  &,i  -  m<5  m  =  2,  3,  4,  (80) 

Bergmann  v  =  3  ®i,2  -  m$  m  =  4,  5,  6,  (81) 

The  highest  convergence  wave  number  is  1  @  and  is  fairly  accurately 
known  for  many  of  these  elements,  from  computation  of  the  observed 
spectral  frequencies.  The  1  @  orbit  accordingly  represents  the  normal 
state  or  energy  level  for  the  ionized  atom  corresponding  to  the  state  1  S 
for  the  normal  atom.  We  shall  consider  as  a  typical  example  the  develop- 
ment of  the  spectra  of  magnesium .  In  Table  XIX  are  listed  the  funda- 
mentally important  wave  numbers  and  equivalent  voltages,  shown 
graphically  in  the  energy  level  diagrams  of  Figures  6  and  7. 

Electronic  impact  at  velocities  below  2.7  volts  gives  rise  to  no  emis- 
sion whatever  in  magnesium  vapor,  the  collision  being  elastic.  Between 
2.7  volts  and  4.33  volts  an  inelastic  impact  corresponding  to  the  first 
resonance  potential  occurs,  displacing  a  valence  electron  to  the  2  p2 
orbit.  The  electron  in  returning  to  the  1  S  orbit  gives  rise  to  the  emis- 
sion of  a  single  line  of  wave  number  v  such  that  hczv  =  eVr'\08  where 
Vr  =  2.7  volts.  The  wave-length  of  this  line  is  X  4571.  The  first 
spectrogram  of  Figure  23,  by  Foote,  Meggers  and  Mohler,  shows  this 
single-line  spectrum  of  magnesium  obtained  with  a  total  applied  po- 
tential of  3.2  volts,  using  the  arrangement  of  electrodes  illustrated  in 
Figure  22. 


LINE  EMISSION  SPECTRA 


119 


TABLE  XJX 

DEVELOPMENT  OF  MAGNESIUM  SPECTRUM 


Series 
Notation 

Wave 
Number 

Volts 

Type  of  Collision 

Type  of  Spectrum 

1  S  -  2  p. 

21871 

2.70 

Inelastic     collision, 

Single-line.     Electron  is    dis- 

at the  lower  reso- 

placed to  2  p2  orbit  and  the 

nance     potential, 

only  possible  return  to  nor- 

1,1 

with  neutral  atom. 

mal  is  by  a  single  transfer 

to  the  1  S  orbit. 

15  -2  P. 

35051 

4.33 

Inelastic     collision, 

Two  lines,  1  S  -  2  P  and  1  S 

at  the  higher  reso- 

— 2  p2.       Electron   is    dis- 

nance   potential, 

placed  to  2  P  orbit  and  must 

with  neutral  atom. 

return  directly  to  1  S,  since 

return  to  2  p  violates  prin- 

ciple of  selection.    Impacts 

at  first  resonance  potential 

also    occur,  giving    rise    to 

1  S  -  2  p2. 

IS. 

61672 

7.61 

Inelastic     collision, 

Complete  arc  spectrum.    One 

' 

with  neutral  atom, 

valence    electron    is    com- 

resulting in  simple 

pletely   removed.       In   re- 

ionization. 

turning  to  normal  all  inter- 

orbital   transitions   consist- 

ent with  the   principle    of 

selection  may  take  place. 

35761 

4.4 

Inelastic     collision, 

Single-line  spectrum   (d  o  u  b- 

35669 

with  simply  ion- 

let).   It  cannot  be  produced 

ized     atom  :     the 

alone  since  simple  ionization 

resonance  poten- 
tial of  the  ionized 

is  first  necessary,  with  the 
resulting    emission    of    the 

atom. 

complete  arc  spectrum. 

1  <3 

121267 

14.97 

Inelastic     collision, 

Complete  enhanced  spectrum. 

with  simply  ion- 

This  accompanies   the   arc 

. 

ized  atom  result- 

spectrum   since    the    atom 

ing  in  ejection  of 

must  be  first  simply  ionized. 

the    second    val- 

There is  no  way  of  main- 

ence electron. 

taining  fixed,  at  reasonable 

temperatures,     an     atmos- 

phere of  simply  ionized  at- 

oms.    Some  are  constantly 

becoming  neutral,  thus  emit- 

ting the  arc  lines. 

121267  + 
61672 

22.8 

Inelastic     collision, 
with  nuetral  atom 

Complete  enhanced  spectrum. 
The  arc  spectrum  should  be 

resulting  in  ejec- 

present also. 

tion  of  both  val- 

ence electrons. 

120 


ORIGIN  OF  SPECTRA 


TABLE  XIX  —  Continued 
DEVELOPMENT  OF  MAGNESIUM  SPECTRUM 


Series 
Notation 

Wave 
Number 

Volts 

Type  of  Collision 

Type  of  Spectrum 

Lai,  2  
Ka 

380000 
95.8  N 

46.9 
1299 

Inelastic  collision, 
with  neutral  atom 
resulting  in  ejec- 
tion of  an  elec- 
tron from  the 
L-orbit. 

Inelastic  collision 

L-radiation,  x-rays. 
Complete  .K-radiation,  x-rays. 

with  atom  result- 
ing in  ejection  of 
an  electron  from 
the  .K-orbit. 

It  is  recalled  that  the  energy  level  2  p  is  really  triplet  in  character,  i.e. 
2  pi,  2  p2,  and  2  p3.  Lines  of  the  wave  numbers  1  S  —  2  pi  and  1  S  — 
2  pz,  however,  have  never  been  photographed  or  observed  visually  for 
any  element  of  this  family.  As  mentioned  in  Chapter  I,  Sommerfeld 
has  attempted  to  explain  this  fact  by  the  use  of  "  internal  quantum 
numbers,"  consideration  of  which  is  beyond  the  scope  of  this  book.  We 
have  never  observed  inelastic  impact  at  voltages  corresponding  to 
1  S  —  2  pi  or  1  S  —  2  ps.  In  magnesium  the  separation  of  this  triplet, 
if  it  existed,  could  not  be  resolved  by  the  methods  employed  for  the 
measurement  of  resonance  potentials,  but  such  is  not  the  case  for  some 
of  the  elements  in  this  family,  for  example  mercury,  where  the  voltages 
should  be  4.5,  4.9  and  5.4.  Our  measurements  gave  4.9  alone.  Accord- 
ingly in  the  present  discussion  we  shall  refer  only  to  the  2  p2  energy 
level.  Recently  Franck  and  Einsporn  have  obtained  indirect  evidence 
of  the  existence  of  these  other  potentials.  If  their  work  be  accepted, 
some  very  interesting  complications  arise,  both  in  theory  and  experiment, 
which  are  considered  later.  So  far,  the  experimental  evidence  of  all 
spectroscopy  has  shown  that  the  2  pi  and  2  ps  orbits  are  occupied  only 
following  the  emission  of  a  line  of  a  subordinate  series  and  a  few  combi- 
nation lines,  for  example  a  transition  of  an  electron  from  an  md  or  an 
ms  orbit,  and  that  the  2  pi  and  2  p3  orbits  do  not  represent  the  initial 
state  in  any  transition  involving  the  emission  of  radiation. 

Returning  to  the  discussion  of  magnesium,  we  find  that  two  types 
of  electronic  impact  between  4.33  and  7.61  volts  may  occur.  The  atom 


LINE  EMISSION  SPECTRA 


121 


may  absorb  2.7  volts  energy  from  the  impacting  electron,  causing  a  dis- 
placement of  a  valence  electron  to  the  2  p2  orbit,  with  the  subsequent 
-  emission  of  X  4571.  The  impacting  electron  retains  the  remaining 
portion  of  its  kinetic  energy  after  rebound  from  the  atom,  suffering 
only  the  velocity  loss  of  2.7  volts.  Secondly,  the  atom  may  absorb 
4.33  volts  energy  from  the  impacting  electron,  causing  a  displacement  of 
a  valence  electron  to  the  2  P  orbit.  On  referring  to  Figure  6  it  is  noted 
that  but  one  energy  level,  2  p.  lies  between  the  state  2  P  and  the  normal 
state  1  S.  Transition  from  2  P  to  2  p  involves  zero  change  in  the 
azimuthal  quantum  number  and  by  the  Bohr  principle  of  selection 
should  not  take  place.  Hence  the  electron  in  the  2  P  orbit  must  return 
to  normal  by  a  single  transition,  resulting  in  the  emission  of  v  —  1  S  — 
2  P,  X  2852.  Accordingly,  on  account  of  the  two  types  of  collision 
present,  we  should  have  between  4.33  and  7.61  volts  a  two-line  spectrum 
consisting  of  the  lines  X  4571  and  X  2852.  This  is  shown  in  the  second 
spectrogram  of  Figure  23,  for  a  potential  of  6.5  volts. 

It  is  of  interest  to  note  that  under  the  conditions  of  this  experiment 
we  have  the  most  favorable  opportunity  for  the  production  of  2  p2  —2P 
if  this  line  represented  a  physically  possible  interorbital  transition. 
Only  two  transitions  from  2  P  are  mathematically  possible,  to  2  p% 
and  to  1  S.  The  line  2  p2  -  2  P  would  lie  at  X  7587.  Using  dicyanin- 
stained  plates  having  high  sensitivity  at  this  wave  length,  not  a  trace 
of  the  line  could  be  detected,  the  two-line  spectrum  appearing  alone. 
This  constitutes  a  very  interesting  verification  of  the  Bohr  principle  of 
selection,. 

Collision  above  7.61  volts  results  in  the  complete  ejection  of  a  valence 
electron.  The  electron  returns  to  the  normal  1  S  orbit  by  successive 
interorbital  transitions,  each  resulting  in  an  emission  of  one  quantum  of 
some  particular  frequency  vk  subject  to  the  condition  laid  down  by 
Equation  (73).  An  individual  atom  accordingly  in  any  single  return 
to  equilibrium  following  ionization,  may  emit  only  a  few  of  the  arc  lines, 
in  rare  cases  only  the  single  convergence  wave  number  1  S,  but  with 
numerous  atoms  approaching  equilibrium  by  the  various  different  com- 
binations of  transitions  possible,  we  have  as  the  macroscopic  result  the 
emission  of  the  complete  arc  spectrum.  This  is  shown  in  the  third 
spectrogram  of  Figure  23,  obtained  at  10  volts. 

If  an  electron  of  4.4  volts  velbcity,  or  greater,  collides  with  an  ionized 
magnesium  atom,  the  single  remaining  valence  electron  may  be  ejected 
from  the  normal  1  @  state  to  the  2  $  state,  as  shown  in  Figure  7,  the 
energy  corresponding  to  4.4  volts  being  abstracted  from  the  impacting 
electron  which  rebounds  from  the  atom  with  the  equivalent  velocity 


122  ORIGIN  OF  SPECTRA 

loss.  The  atom  in  assuming  its  equilibrium  state  as  a  positive  ion 
accordingly  emits  the  pair  1  @  -  2  $i,2,  X  2796  -  2802.  This  is  the 
"single-line"  spectrum  of  ionized  magnesium,  a  doublet,  analogous  to 
the  single- doublet  spectra  of  the  alkalis,  considered  later.  It  requires 
for  its  excitation  the  preliminary  ionization  of  the  atom  for  which  a  7.61 
volt  collision  is  necessary.  Hence  it  will  appear  only  at  potentials 
greater  than  7.61  volts  although  the  pair  itself  requires  but  4.4  volts 
for  its  excitation.  Two  successive  collisions  are  necessary,  the  first 
resulting  in  ionization  of  the  normal  atom,  and  the  second  correspond- 
ing to  a  resonance  potential  of  the  atom-ion.  The  pair  appears  clearly 
in  the  10  volt  spectrogram  of  Figure  23. 

If  an  electron  of  14.97  volts  velocity,  or  greater,  collides  with  an 
ionized  magnesium  atom,  the  single  remaining  valence  electron  may  be 
completely  ejected,  leaving  the  atom  doubly  ionized.  The  electron 
returns  to  the  normal  1  @  orbit  of  the  simply  ionized  atom  by  successive 
interorbital  transitions,  each  resulting  in  an  emission  of  one  quantum  of 
some  particular  frequency  fc  (subject  to  the  condition  laid  down  by 
Equation  (75)  where  V*  =  14.97  volts J  For  many  atoms,  the  com- 
posite result  is  the  emission  of  all  the  enhanced  or  spark  lines,  the  com- 
plete doublet  spectrum  of  magnesium.  This  is  shown  by  the  last  three 
spectrograms  of  Figure  23.  Over  thirty  well  known  enhanced  lines 
belonging  to  series  are  readily  visible  in  the  original  negatives  of  these 
illustrations.  The  wave-lengths  of  some  of  the  more  prominent  lines 
are  indicated  in  the  figure. 

At  22.8  volts,  corresponding  to  1  @  +  1  S,  there  is  a  possibility  of 
doubly  ionizing  magnesium  in  a  single  electronic  collision.  With  any 
mechanical,  symmetrical  model  of  a  heavy  atom,  it  is  rather  difficult 
to  see  how  this  could  occur,  and  as  yet  no  one  has  shown  that  an  increase 
in  radiation  takes  place  at  this  velocity.  However,  the  numerical 
value  is  of  importance  in  thermochemical  relations  as  it  gives  the  total 
work  of  double  ionization  regardless  of  how  the  process  is  effected. 

At  46.9  volts  and  J.299  volts,  respectively,  the  L  and  K  x- radiations 
appear  (cf .  Chapter  IX)*  Apparently  no  change  in  the  visible  radiation 
occurs  as  the  voltage  46.9  is  exceeded.  One  should  expect  to  find  the 
spectrum  of  doubly  ionized  magnesium  in  this  voltage  range.  Possibly 
a  difficulty  in  producing  such  spectra  is  the  small  probability  of  the 
three  successive  collisions  necessary,  where  the  energies  absorbed  from 
the  impacting  electrons  have  wide  variation.  In  this  case  we  require 
7.61,  14.97  and  a  value  slightly  exceeding  46.9  volts,  the  excess  arising 
in  the  fact  that  removal  of  two  outer  electrons  produces  some  effect  on 
the  work  required  to  eject  an  L-electron. 


LINE  EMISSION  SPECTRA 


123 


The  foregoing  discussion  outlines  the  fundamental  stages  in  the 
excitation  of  the  spectra  of  magnesium  by  electronic  impact.  We  have 
yet  to  consider  certain  auxiliary  processes  which  involve  absorption  of 
radiation  followed  by  electronic  impact  or  processes  which  involve  two 
successive  electronic  collisions,  as  mentioned  on  page  115,  items  (2) 
and  (3). 

If  the  current  density  is  high,  fundamental  lines  of  the  subordinate 
series  may  be  excited  below  the  ionization  potential,  in  addition  to  the 
two-line  spectrum.  A  valence  electron  of  the  normal  atom  is  ejected 
to  the  2  p2  orbit  by  direct  impact  or  more  probably  by  absorption  of 
radiation  of  wave  number  1  S  —  2  p%  emitted  by  a  neighboring  atom 
which  is  previously  excited.  Before  the  first  atom  can  assume  equilib- 
rium, with  the  resulting  radiation  1  S  —  2  p%,  it  collides  with  an  electron 
and  the  valence  electron  is  displaced  to  a  higher  energy  level,  for  ex- 
ample 1  s,  2  s,  3  d,  etc.  From  these  energy  levels  the  electron  may  fall 
to  2  pi,  2  p2  or  2  p3,  giving  rise  to  subordinate  series  triplets.  Thus  we 
have  observed  at  7  volts  in  addition  to  1  S  —  2  P  and  1  S  —  2  p2  the 
following  lines  of  subordinate  series  of  magnesium. 


Notation 

\ 

2pi 

-  2s 

3336 

2p, 

-  3d 

3838 

2p2 

-3d 

3832 

2p3 

-  3d 

3829 

2j>, 

-  Is 

5183 

2p2 

-  Is 

5173 

2p3 

-  Is 

5168 

For  a  similar  reason  we  find  lines  of  the  subordinate  series  of  the 
enhanced  spectrum  below  14.97  volts,  the  potential  required  to  remove 
the  second  electron  and  produce  double  ionization.  In  the  original 
negative  for  the  10  volt  spectrogram9  of  Figure  23  the  following  enhanced 
lines  of  subordinate  series  are  prominent  in  addition  to  the  single- 
doublet  spectrum  1  @  —  2  $1,2. 


Notation 

X 

2?!-  3® 

2  %  -  3  2) 
2  ?i  —  2  @ 
2  $2  -  2  @ 

2798 
2790 
2936 

2928 

! 

9  See  Phil.  Mag.,  42,  1006  (1921),  Table  I,  for  a  complete  analysis  of  these  spectrograms. 


124  ORIGIN  OF  SPECTRA 

The  simply  ionized  atom  absorbs  radiation  of  wave  number  1  @  —  2  $i,2 
and  before  it  can  assume  equilibrium  and  emit  this  pair,  it  collides  with 
an  electron.  The  remaining  valence  electron  is  displaced  to  an  outer 
orbit  such  as  2  @  or  3  2),  in  which  states  the  ionized  atom  is  capable  of 
emitting  the  above  listed  lines. 

This  development  of  the  spectrum  of  magnesium  is  typical  of  all 
the  metals  of  this  group  of  the  periodic  table.  Franck  and  Hertz,10 
working  with  mercury  vapor,  were  the  first  to  obtain  a  single-line  spec- 
trum. Nearly  every  one  who  has  made  photographs  at  low  voltage  has 
since  observed  X  2537  as  a  single  line,  the  vapor  frequently  occurring 
as  an  impurity  in  spectra  of  other  vapors,  when  not  produced  inten- 
tionally. We  have  observed  the  single-line  and  two-line  spectrum  of 
zinc  as  an  impurity  in  magnesium.11  McLennan  and  Henderson12  show 
photographs  of  the  single-line  spectra  of  mercury,  cadmium  and  zinc. 
They  also  in  1915  observed  that  the  complete  arc  spectrum  appeared 
slightly  above  the  ionization  potentials,  the  values  of  which  were  un- 
known at  this  date.  McLennan  and  Ireton13  show  photographs  of 
the  two-line  spectra  of  zinc  and  cadmium.  No  investigations  of  the 
enhanced  spectra  in  the  low  voltage  arc  for  metals  of  Group  TI,  aside 
from  magnesium,  have  been  published,  a  problem  upon  which  Dr. 
Meggers  and  the  authors  are  engaged  at  the  present  time.  However, 
the  critical  frequencies  are  fairly  accurately  known  from  spectroscopic 
data,  except  for  mercury  and  radium.  We  are  accordingly  able  to 
summarize  completely  in  Table  XX  the  successive  stages  of  develop- 
ment in  the  spectra  of  these  elements,  excited  by  electronic  impact. 
This  table  gives  all  the  spectra  arising  in  disturbances  of  the  valence 
electrons,  which  the  atom,  in  the  absence  of  a  magnetic  or  electric  field, 
is  capable  of  emitting. 

RELATION  BETWEEN  1  @  AND  1  S 

There  appears  to  be  a  definite  relation  of  some  physical  significance 
between  the  limiting  frequencies  1  @  and  1  S.  In  Table  XXI  are  given 
the  values  of  the  ratio  1  @  /I  S,  using  the  data  of  Table  XX. 

The  physical  significance  of  this  ratio  can  be  roughly  obtained  in 
the  following  manner.  Referring  to  Table  III,  the  magnesium  atom  is 
seen  to  consist  of  three  shells  of  electrons  in  the  arrangement  2,  8,  2. 
By  means  of  an  equation  similar  to  (51)  we  shall  compute  the  total 

"Verb.  Physik.  Ges.,  16,  p.  512  (1914). 

11  Foote,  Meggers  and  Mohler,  Phil.  Mag.,  42,  p.  1014  (1921) 

»  Proc.  Roy.  Soc.,  91,  pp.  485-91  (1915). 

«  Phil.  Mag.,  36,  pp.  461-71  (1918). 


LINE  EMISSION  SPECTRA 


125 


.S.-5  S  o 

'    - 


C<l  rH 

00  <N 

i—"  00 


rtH  (N 

"fi  »o 

*O  o> 

fc»  •    •    CP 

^  00 


40 


S3 


O  co  i 

1& 


ll'!| 


rH  Oi         OO5 
CO  IO         CO  C^' 


00  "* 

id  id 


Q 


rH  O5  Tf^  C^J  IO(M  t^lO 

COCO  rHOi          IOOO          rHrH 

t^  CO  -^  rH 

•C  iO  IOIO 

COCO  <N  (N 


00  CO 

rH  CO 


Tt<   CO 


(M_  CO 
CO(N 


<N  CO 
(M  C^ 


g 


Jill 

sir 


CO  O 

^  CO 


1^1' 

0     ^ 


9-     8 


1111 


s 


8 


OJU 

^  t.  &d 

'3    0)  ^(M 

'I  ^  S  I 


fafi 

c» 


113 

fill 


00  rH  O5 

00  O  l> 


«H  •      co 


rH  O  g  Tg 

00  C<l  IO  XO 


s     s 


Q     "" 


M 


O 


_ 

02 


O 


126 


ORIGIN  OF  SPECTRA 


energy  of  the  outer  ring  (1)  TF2  with  both  valence  electrons  and  (2) 
Wi  with  one  valence  electron. 


wr=  - 


(82) 


(83) 


(84) 


The  value  Wz  represents  the  work  required  to  remove  both  valence 
electrons  and  is  accordingly  proportional  to  1  @  +  1  <S.  The  value  Wi 
represents  the  work  required  to  remove  the  second  valence  electron 
after  the  first  has  been  ejected  and  is  accordingly  proportional  to  1  @. 
Hence : 


2(2  -  0.25)2 


W  i 


=  1.531, 


•and 


(85) 


This  value  agrees  approximately  with  that  given  in  Table  XXI.  Similar 
computations  for  the  other  elements  lead  to  the  same  numerical  relation. 
The  value  1  @  for  mercury  in  Table  XX  was  obtained  in  this  manner 
from  the  known  magnitude  of  1  S,  since  the  series  relations  in  the  en- 
hanced spectrum  are  unknown. 

TABLE  XXI 
RATIO  1  @/l  S  FOR  METALS  OF  GROUP  II 


Element 

re/is 

Mg 

1.97 

Ca 

1.94 

Zn 

1.95 

Sr 

1.94 

Cd 

1.93 

Ba 

1.92 

Mean  1.94 

LINE  EMISSION  SPECTRA  127 

METALS  OF  GROUP  I  OF  THE  PERIODIC  TABLE 
The  metals  of  Group  I  as  shown  in  Table  X  all  have  a  single  resonance 
potential.  We  accordingly  find  a  three-stage  development  in  the 
spectra.  A  single-line  or  more  precisely  a  single-doublet  spectrum, 
1  s  —  2  pi, 2,  appears  at  the  resonance  potential.  The  complete  arc 
spectrum  is  excited  at  the  ionization  potential  and  at  a  still  higher 
potential  the  enhanced  spectrum  appears. 

There  is  no  reason  in  the  Bohr  theory  why  resonance  potentials  of 
higher  magnitudes,  corresponding  to  1  s  —  3  pi,2,  1  s  —  4  pi,2,  etc., 
should  not  exist,  a  statement  applying  equally  well  to  the  metals  of 
Group  II.  Thus  we  might  expect  that  the  valence  electron  could  be 
displaced  from  the  normal  1  s  orbit  directly  to  any  mp  orbit  as  a  result 
of  inelastic  collision  with  the  proper  energy  exchange.  In  the  complete 
arc  spectrum  the  intensity  of  1  s  —  2  p  is  many  times  greater  than  that 
of  1  s  —  3  p.  In  fact  in  every  series,  the  intensity  of  the  lines,  referred 
to  absolute  value  from  which  plate-  or  eye-sensitivity  is  eliminated, 
decreases  rapidly  from  the  first  term  to  zero  at  the  convergence.  Now 
it  seems  possible  that  just  as  the  probability  of  the  transfer  of  the  valence 
electron  from  an  mp  orbit  to  the  1  s  orbit  evidently  decreases  rapidly 
as  m  increases,  so  the  probability  of  the  displacement  of  the  valence 
electron  to  an  mp  orbit  as  a  result  of  electronic  collision  with  a  normal 
atom  may  decrease  as  m  increases,  even  though  all  the  impacting 
electrons  have  a  velocity  corresponding  to  1^  s  —  mp.  If  this  were  so, 
these  higher  resonance  potentials  might  exist  and  not  be  detectable  by 
the  ordinary  methods  of  measurement.  For  example  if  one  hundred 
collisions  resulting  in  a  displacement  of  the  valence  electron  to  2  p 
occurred  while  one  collision  resulted  in  a  displacement  to  the  3  p  orbit,  the 
effect  of  the  latter  would  be  nearly  indistinguishable  by  the  electrical 
methods  employed  in  the  investigation  of  inelastic  impact.  On  the 
other  hand  one  collision  of  the  3  P  type  in  a  hundred  or  more  of  the  2  p 
type  should  produce  an  observable  spectroscopic  effect. 

Referring  to  Figure  5,  electronic  displacements  to  the  3  p  orbit 
enable  the  vapor  to  emit  1  s  —  3  p,  the  second  pair  of  the  principal 
series,  besides  the  first  pair  and  infra-red  lines  representing  the  indirect 
transition  from  .3  p  to  2  p,  and  the  first  pair  of  each  subordinate  series. 
The  various  lines  which  may  be  emitted  following  a  displacement  to 
J*  p  i  are  summarized  in  Table  XVII .  At  the  inelastic  impact  correspond- 
ing to  l_s_—  3  p  we  should  accordingly  observe  the  emission  of  the 
following  more  important  pairs:  Is  —  2  p,  Is  —  3  p,  2  p  —  2  s  and 
2  p  -  3  d. 


128 


ORIGIN  OF  SPECTRA 


Foote  and  Meggers14  attempted  to  investigate  this  for  caesium. 
Unfortunately  for  this  element  the  latter  two  pairs  lie  in  the  far  infra- 
red and  could  not  be  observed.  The  wave  number  Is—  2  pi  corre- 
sponds to  1.4  volts;  1  s  —  3  pi  to  2.7  volts;  1  s  —  4  pi  to  3.2  volts;  1  s  — 
5  pi  to  3.4  volts;  and  1  s  to  3.9  volts.  The  ratio  of  absolute  intensities 
of  the  lines  (1  s  —  2  pi)  -r-  (1  s  —  3  pi)  i.e.  X  8521/X4555  were  measured 
for  a  series  of  accelerating  potentials  as  follows : 


Volts 

7 

4 

3.8 

3.4 

3.2 

2.8 

X  8521/X4555  

350 

2100 

8300 

10500 

>  10000 

==  00 

Accordingly  at  voltages  less  than  3.9,  the  ionization  potential,  and 
greater  than  2.7,  corresponding  to  1  s  —  3  p,  there  appears  to  be  no 
emission  of  1  s  —  3  pi,  X  4555,  which  cannot  be  attributed  to  ionization. 
At  3.4  volts  for  example  the  intensity  of  1  s  —  3  p\  is  but  1/10000  that 
of  1  s  —  2  pi,  although  all  the  electrons  have  a  velocity  sufficient  to 
eject  the  valence  electron  to  the  3  pi  orbit. 

The  electrons  emitted  by  a  heated  cathode  (equipotential  surface) 
have  a  velocity  distribution  given  by  Maxwell's  law.  It  may  be  readily 
shown  that  on  account  of  this  temperature  distribution,  the  fractional 
number  F  of  emitted  electrons  having  a  velocity  greater  by  F0  than 
the  applied  potential  V  is: 


erfx  +  -L  e~*t 
VTT 


where  x2  =  11600  V0/T  , 


(86) 


where  T  is  the  absolute  temperature  of  the  cathode.  At  a  dull  red 
heat  about  30  electrons  per  10,000  have  a  velocity  0.5  volt  greater  than 
V.  One  in  10,000  should  be  sufficient  to  account  for  the  intensity  of 
X  4555  at  3.4  volts.  Similar  conclusions  may  be  drawn  from  observa- 
tions on  other  lines.  For  example  the  line  2  pi  —  5  d,  X  6974,  was  found 
by  absolute  intensity  measurement  to  be  of  such  low  intensity  below 
the  ionization  potential  that  its  excitation  may  be  explained  by  the 
small  number  of  high  velocity  electrons  present.  No  line,  other  than 
the  pair  1  s  —  2  p,  shows  a  rapid  increase  in  intensity  when  the  velocity 
of  the  electrons  reaches  that  corresponding  to  its  particular  energy  level. 
Hence  we  conclude  that  the  valence  electron  may  be  ejected  only  to  the 
2  p  orbit,  following  electronic  impact  with  the  normal  atom,  thus  con- 
firming the  data  obtained  by  direct  measurement  of  critical  potentials. 

"  Bur.  Standards  Sci.  Paper  No.  386  (1920). 


128  A 


ll 


3  * 
8,1 

o    ^ 

s  * 


CB     ° 

O5     ^ 

S 

^ 


LINE  EMISSION  SPECTRA  129 

As  the  electronic  velocity  is  increased  above  that  corresponding 
to  the  resonance  potential,  we  have  the  emission  of  1  s  —  2  p.  As  soon, 
however,  as  the  ionization  potential  is  reached  all  arc  lines  are  emitted. 
If  an  atom  emits  any  line  of  the  principal  series  beyond  1  s  —  2  p,  it  can- 
not at  the  same  time  emit  1  s  —  2  p,  as  seen  from  Figure  5.  Hence 
electrons,  which  just  below  the  ionization  potential  give  rise  to  1  s  —  2  p, 
just  above  ionization  produce  other  principal  series  lines  at  the  sacrifice 
of  1  s  —  2  p.  There  should  be  accordingly,  for  the  same  current,  a 
decrease  in  the  intensity  of  1  s  —  2  p,  as  the  ionization  potential  is 
passed,  a  fact  confirmed  by  direct  experiment. 

The  intensity  of  each  line  above  the  ionization  potential  was  ob- 
served to  be  approximately  proportional  to  the  number  of  electrons 
leaving  the  cathode.  This  follows  from  the  quantum  theory.  The 
number  of  electronic  collisions  and  hence,  roughly,  the  number  of  quanta 
of  any  particular  frequency  is  proportional  to  the  number  of  electrons  or 
approximately  proportional  to  the  total  current,  a  fact  substantiated 
earlier  by  Jolly  and  other  investigators. 

This  work  on  caesium  should  be  repeated,  using  a  3-electrode  instead 
of  2-electrode  discharge  tube,  and  should  be  extended  to  other  metal sr 
especially  mercury.  The  foregoing  is  by  no  means  conclusive,  for 
quantitative  spectrophotographic  measurements  at  and  slightly  above  the 
threshold  value  of  the  plate  are  exceedingly  difficult  if  not  impossible.15 

Foote  and  Meggers16  show  photographs  of  the  single-doublet  spectrum 
of  caesium,  X  8521  and  X  8943  at  the  resonance  potential,  and  the  com- 
plete arc  spectrum  slightly  above  the  ionization  potential.  The  single- 
doublet  emission  spectra  of  the  alkalis  are  precisely  the  absorption  lines 
shown  in  Figure  15,  the  pair  1  s  —  2  pi  and  1  s  —  2  p2.  The  authors 
and  Dr.  Meggers,17  using  the  design  of  Figure  22,  have  obtained 
photographs  illustrating  the  successive  stage  development  in  the  spectra 
of  sodium  and  potassium,  the  latter  being  reproduced  here  as  Figure  24. 

With  potassium,  from  1.60  to  4.32  volts,  we  have  the  single  pair  X 
7664  and  X  7699,  as  seen  in  the  first  spectrogram.  From  4.32  to  about 
20  volts  the  arc  spectrum  consisting  of  the  series  of  doublets  represented 
by  Equations  (34)  to  (37)  are  excited,  as  seen  in  the  second  and  third 
spectrograms.  Above  about  20  volts  the  enhanced  lines  are  prominent, 

15  Dr.  C.  E.  Kenneth  Mees,  Director,  Eastman  Kodak  Research  Laboratory,  where 
every  conceivable  means  and  instrument  for  spectrophotographic  analysis  are  at  hand, 
together  with  a  staff  trained  in  the  technique  of  plate  sensitometry,  hi  1920  stated  that  it 
was  a  fixed  policy  of  their  laboratory  not  to  rely  on  spectrophotographic  photometry  for  such 
types  of  problem,  if  other  methods  are  possible.  It  is  certainly  doubtful  if  any  laboratory  not 
specially  equipped  for  such  work  can  hope  to  secure  unquestionable  results. 

is  Loc.  cit. 

"  Foote,  Meggers  and  Mohler,  Astrophys.  J.,  55,  pp.  145-61  (1922). 


130  ORIGIN  OF  SPECTRA 

appearing  in  the  last  two  spectrograms.  Several  hundred  lines  are 
readily  visible  on  the  original  negatives. 

The  third  spectrogram  shows  the  pair  1  s  —  3  d,  which  as  mentioned 
on  page  36  is  an  exception  to  the  principle  of  selection,  since  the  change 
in  azimuthal  quantum  number  is  two  units.  Here  the  presence  of  the 
line  cannot  be  attributed  to  an  incipient  Stark  effect,  since  there  is  no 
applied  field  in  the  space  between  the  grid  and  plate  of  Figure  22.  The 
corresponding  pair  in  sodium  is  similarly  excited.  These  exceptional 
lines  appear  at  high  current  density,  and  the  physical  basis  for  their 
excitation  is  still  an  open  question.18 

With  sodium,  from  2.09  to  5.12  volts  we  have  the  single-pair,  the 
D-lines.  From  5.12  to  about  35  volts  the  complete  arc  spectrum  appears, 
while  above  35  volts  the  many-line  enhanced  spectrum  is  excited. 

The  enhanced  spectra  of  the  alkalis  should  resemble  the  arc  spectra 
of  the  rare  gases.  In  the  richness  and  complexity  of  the  lines  the  re- 
semblance fulfils  all  expectations.  As  yet,  however,  no  series  relations 
have  been  determined.  It  is  nevertheless  possible  to  roughly  estimate, 
theoretically,  the  potentials  required  to  excite  these  enhanced  lines. 
Referring  to  Table  III,  for  sodium,  we  have  the  K-ring  with  2  electrons, 
the  L-ring  with  8  electrons  and  the  outer  ring  with  the  single  valence 
electron.  Suppose  the  valence  electron  is  removed  by  a  5.1  volt  elec- 
tronic impact  and  then  an  electron  is  removed  from  the  L-orbit,  thus 
leaving  the  atom  doubly  ionized.  The  atom  is  now  ready  to  emit  any 
line  of  the  enhanced  spectrum.  Suppose  that  the  highest  convergence 
frequency  in  the  enhanced  spectrum  is  emitted.  Would  this  involve 
the  return  of  an  electron  from  without  the  atom  to  the  L-ring  from 
which  it  was  originally  ejected?  There  is  some  reason  for  believing  that 
the  electron  should  assume  an  orbit  outside  the  shell  of  seven,  forming 
a  metastable  sodium  ion.  That  is,  two  kinds  of  simply  ionized  sodium 
atoms  may  exist  with  electrons  distributed  in  shells  as  follows : 


1st 

2d 

3d   Shell 

2 

8 

2 

7 

1 

The  first  type  is  in  a  state  preliminary  to  the  emission  of  the  arc  spec- 
trum; the  second  type  is  in  the  normal  state  for  the  absorption  of  principal 

18  Possibly  it  has  something  to  do  with  the  interaction  of  atomic  fields  of  neighboring 
atoms  and  ions.  This  suggestion  was  made  by  the  authors,  Phil.  Mag.,  43,  pp.  659-61  (1922), 
and  later  was  affirmed  by  Bohr,  Phil.  Mag.,  43,  pp.  1112-16  (1922),  in  discussion  of  the  paper. 


LINE  EMISSION  SPECTRA  131 

series  enhanced  lines,  a  state  corresponding  to  1  @  of  the  ionized  alkali 
earths.  In  the  second  arrangement,  the  single  outside  electron  revolves 
in  a  quantized  orbit  of  unit  azimuthal  quantum  number,  about  the 
nucleus  and  the  nine  remaining  electrons. 

Proceeding  by  a  method  identical  with  that  used  in  the  derivation 
of  the  Ritz  equation,  page  32,  we  shall  compute  the  energy  required  to 
eject  the  outer  electron  in  the  configuration!^:  7:1.  ~~ 


Let  p  =  number  of  electrons  in  inner  ring,  radius 

g=        "        "       "          "    2d       "    radius  a2^ 

atomic  no.  =  Z  =  p  +  q  +  k  where  k  =_2_for  spark  spectra  and  1  for 

arc  spectra. 


e 
where  ci  =  T  (Pa^  +  2<*24).  -f  JJ        (88) 

4  > 

Performing  the  quantum  integration  as  in  Equations  (28)  and  (29) 
we  obtain: 

W=_NM* 

(na  +  nr  +  a)2 

(2  TT^  mWkci 

where  a  =  v '—^T. — -  -  (90) 

na*h4 

For  the  normal  state  na  +  nr  =  1^  and  expressing  our  values  in  volts, 
we  find  from  Equation  (89) : 


Normal  state          V  =  7J^r^2  '  (91) 

Eliminating  ai  and  a2  from  Equation  (88)  by  use  of  Equations  (47)  to 
(49)  we  obtain  from  Equation  (90)  when  na  +  nr  =  1 

_fcr      P.  leg 


On  account  of  the  assumptions  involved  in  the  derivation  of  Equation 
(92),  coplanar  orbits,  etc.,  it  should  not  be  expected  that  it  would  yield 
exact  numerical  magnitudes.  But  by  applying  Equations  (91)  and 
(92),  first  to  arc  spectra  and  then  to  sgark__sgectra?  the  ratios  a* /a 
and  V*/V  may  possess  some  physical  significance.  Substituting  the 
value  of  V,  the  simple  ionization  potential,  in  Equation  (91)  and 
solving.,fpr  a  where^j=_l,  we  may  compute  a*  from  the  ratio  a* /a  ob- 
tained through  Equation  (92),  and  then  by  Equation  (91)  compute  V* 


132 


ORIGIN  OF  SPECTRA 


where  k  =  2.  We  thus  obtain  the  value  of  the  work,  expressed  in  volts, 
necessary  to  remove  the  second  electron  from  its  quantized  orbit  in  the 
simply  ionized  sgdiiini  atom.  The  equations  are  equaHjT  applicable 
to  the  other  alkalis.  We  accordingly  compute  the  following  table: 


Element 

a*/a 

V* 

Na 

1.50 

14 

K 

1.50 

11 

Rb 

1.66 

10 

Cs 

1.68 

9 

These  voltages  should  correspond  approximately  to  the  highest  con- 
vergence frequencies  of  the  spark  spectra. 

In  the  case  of  sodium,  for  example,  the  complete  spark  spectrum 
requires  for  its  excitation  the  removal  of  one  L-electron  corresponding 
to  the  work  La  =  35  volts,  as  shown  in  Chapter  IX,  followed  by  a  14 
volt  collision  through  which  the  outer  electron  is  removed.  The  total 
work  required  to  remove  both  electrons  is  equivalent  to  the  sum  of  these 
voltages  or  49  volts.  The  process  may  be  effected  in  the  reverse  order; 
removal  of  the  valence  electron  requiring  5  volts  followed  by  removal  of 
the  L-electron  at  44  volts,  the  sum  necessarily  being  the  same.  The 
enhanced  spectrum  should  accordingly  begin  to  appear  in  an  arc  at 
about  35  volts.  Now  by  three  successive  impacts  resulting  in  (1) 
ejection  of  valence  electron,  (2)  transition  of  L-electron  to  new  quantized 
orbit,  (3)  ejection  of  the  electron  from  this  new  orbit,  the  enhanced 
spectrum  might  appear  at  a  somewhat  lower  voltage.  However,  since 
three  successive  impacts  are  in  general  improbable,  we  may  conclude 
that  the  enhanced  spectrum  of  sodium  accompanies  its  L-radiation, 
at  the  minimum  voltage  corresponding  to  La  =  35.  This  conclusion  is 
substantiated  by  the  work  of  Dr.  Meggers  and  the  authors. 

In  a  similar  manner,  the  enhanced  spectrum  of  potassium  should 
accompany  its  M -radiation  appearing  at  the  minimum  voltage  Ma. 
As  shown  in  Chapter  IX,  Ma  =  20  to  23  volts.19  We  see  in  Figure  24 
that  the  enhanced  lines  have  put  in  their  appearance  at  25  volts,  con- 
firming the  above  deductions. 

Likewise,  the  enhanced  spectra  of  rubidium  and  caesium  should 
accompany  their  N  and  0  x-radiation  respectively.  No  data  exist 
relative  to  either  these  x-rays  or  the  excitation  potentials  for  the  en- 
hanced spectra. 


19  Mai, 2  =  20.     When  the  limits  are  complex,  probably  the  lower  value  is  effective. 


PLINE  EMISSION  SPECTRA  133 

We  may  contrast  the  behavior  of  the  alkalis  and  the  alkali  earths. 
Simple  ionization  of  the  latter  leaves  the  atom  in  a  normal  state  for  the 
absorption  of  enhanced  lines,  in  a  state  where  the  remaining;  valence 
electron  occupies  the  1  @  orbit.  Simple  ionization  of  the  alkali,  however, 
does  not  do  this.  As  a  consequence  the  entire  enhanced  spectrum  of  an 
alkali  earth  appears  at  the  potential  V*  corresponding;  to  1  @,  whereas 
it  requires  a  potential  somewhat  greater  than  F*  to  excite  the  enhanced 
spectrum  of  an  alkali.  For  example,  in  sodium,  although  V*  =  14 
volts,  the  enhanced  lines  do  not  appear  below  La  =  35  volts.  Similarly 
with  potassium:  although  F*  =  11  volts,  it  requires  20  volt  electronic 
impact  to  produce  the  enhanced  lines. 

Table  XXII  summarizes  the  development  in  the  spectra  of  metals 
of  Group  I,  excited  by  electronic  discharge. 

THE  RARE  GASES 

The  spectra  of  the  rare  gases,  except  ionized  helium,  are  character- 
ized by  exceedingly  complicated  combination  systems  of  series  lines. 
Most  of  the  fundamentally  important  lines  should  lie  far  in  the  ultra- 
violet, in  many  cases  beyond  the  range  of  the  vacuum  spectrograph. 

Helium. — As  seen  from  Table  XIV  helium  has  an  ionization  potential 

{>  about  25.5  volts  and  two  resonance  potentials  at  20.4  and  21.2  volts. 

If  we  could  reason  by  analogy  to  the  alkali  earths,  we  should  expect  a 

single  line  spectrum.  X  603,  at  20.4_vplts  and  a  two-line  spectrum,  X  603 

I  and  X  580  at  2J.2  volts.     However,  as  discussed  in  the  section  on  "The 

Normal  Helium  Atom,"  Chapter  III,  only  the  line  585  is  known,  and 

the  true  significance  of  and  nomenclature  for  this  line  is  possibly  a 

matter  of  doubt.     We  are  accordingly  unable  to  draw  any  conclusion 

in  regard  to  the  excitation  of  helium  lines  below  the  ionization  potential.20 

The  work  of  double  ionization  of  Bohr's  normal  coplanar  helium 

atom  should  be  83  volts,  as  shown  by  Equation  J$5).    We  have  seen  that 

this  configuration  is  incorrect,  since  it  gives  28.8  instead  of  25.5  for  the 

ionization  potential.    We  may,  however,  readily  determine  the  work 

required  to  remove  the  second  electron  after  the  first  has  been  ejected. 

J  This  value,  computed  from  Equation  (20)  by  putting  Z  =  2,  is  54.2 

volts.     Hence  the  correct  value  for  the  work  of  double  ionization  is 

7  54.2  +  25.5  or  79.7  volts.21 

2°Franck  and  Knipping's  work,  as  discussed  on  page  73,  Indicates  the  presence  of 
15  —  2P  and  IS  —  3P  below  ionization.  See  also  important  foot  note  39,  page  77,  added  since 
book  was  in  page  proof. 

21  Possibly  79.5  is  a  closer  value. 


134 


ORIGIN  OF  SPECTRA 


I 


1! 

o 


- 
- 
CQ 


V 

g 

1             T^           r-H                            O              I             O5 
1            i-H           T-H                          i-H              1 

1 

gfiw- 

& 

ex 
02 

|8i 

|lll 
.a*s  -g> 

(N         10         0        g        c-         S 

CO        CO        CM         2 

1 

S££ 

! 

.1   MS 

O 

<N         *e»                         * 

•a  >-g'-3 

l*Jj 

^    ^~*f-< 

S     ;?     ;?            *« 
«      e»2vS^^      e      e 

^K^^I^^^OO 

o 

so 

^ 

3 

E 

fill 

l>.(MC<IG5COTt<OOCi 

COrHCOCOTH^OOO            Q 

I 

fir 

00 

£ 

M 

O 

.a    v. 

c— 

"S 

S 

]3  o>  ^ 

p^        O^        CO         OO        O^         P^        iO         C^ 
GO         Tj^         f^         ^^         oO         O»*         ^^         ^^* 

6 

f    S5 

TfTFCOCOCOCOCOI> 

P 

a  g-a 

1111 

TJH        O        I-H        O        00        CO        *O 

OOi-HCOCOlOt>-'^t|T-H 

S  *S  "*"*  ^ 

THCCJT-5c6i-HCOi-HlO 

^j   X  ^? 

^ 

E 

Sw^ 

I 

^ 

iq 

-4-3 

0) 

c<» 

SCO        ^O        ^O        O5        O^        00        O^ 
^O         00         CO        l>         ^O        l>-        iO 

3 

1 

|          I 

1         - 

O5        O5         O5         >O         tO         *O        I-H         CO 
^         CO         C^         O         CM         O5         i-H         t>» 
T-HT-HT—  icOi-HCMT—  ICO 

j. 

h» 

n 

g 

f-t 
V                 - 
r*                  ?^c 

00 

o3 

|>                <^ 
1 

COCOCO^I^CO<NrtH 
O^         O^         ^^        1s*         QO        ^J^         t^        ^H 

^JH           CO           CO           C^           C^l           ^^           T~  H           T'H 

i-H 

1-HT-HT-HCOT-HCOT-HTtl 

-I-S 

^                            ^          i^J            bC           DQ            ^ 

3r^iMOPH<1O<1 

LINE  EMISSION  SPECTRA 


135 


Accordingly,  the  arc  lines  represented  by  Figure  10  should  appear 
at  a  potential  of  25.5  volts.  Spark  lines  should  be  excited  at  54.2  volts 
in  case  the  impacting  electron  collides  with  a  simply  ionizexi  atom.  A 
79.7  volt  electron  is  capable  of  doubly  ionizing  the  normal  atom  so  that 
an  increase  in  intensity  of  the  spark  lines  may  take  place  at  this  voltage. 

We  have  seen  from  Figure  2  that  the  wave-lengths  and  even  the  fine 
structure  of  the  spark  lines  are  accurately  given  by  Equation  (22)-  r  ^ 
The  mean  wave-length  of  each  spark  line  is  fairly  closely  representea 
by  the  simpler  Equation  (9')  in  which  the  higher  order  terms  of  Equa- 
tion (22)  are  omitted: 

<ft(> 


Table  XXIII  gives  the  computed  wave-lengths  for  the  first  and  second 
terms  and  convergence  of  each  of  the  four  series  where  n  =  1,  2,  3,  4 
respectively.  In  a  general  way  the  first  series  corresponds  to  the 

TABLE  XXIII 
IMPORTANT  ENHANCED  LINES  OF  HELIUM 


Line 

*MH) 

'MHO 

'MH) 

<MM) 

m 

\(vac) 

m 

\(vac) 

m 

X(oir) 

m 

X(oir)       /££>- 

First  

2 
3 

00 

304  A 
256 

228 

3 
4 

00 

1640  A 
1215 
911 

4 
5 

00 

4686  A 
3203 
2050 

5 
6 

00 

10124  A 
6560 
3644 

Second  

Convergence  

Corresponding 
series  in  hydrogen 

Lyman 

Balmer 

Paschen 

Brackett* 

*  Of.  Nature,  109,  p.  209  (1922). 

principal  doublet  enhanced  series  of  the  alkali  earths  and  the  second 
series  to  the  subordinate  doublet  series  of  these  metals,  while  the  direct 
observations  on  the  excitation  potential  for  the  enhanced  lines  of  helium 
are  confined  to  the  line  X  4686  of  the  third  series.  We  may  be  certain, 
however,  if  the  latter  appears,  the  lines  of  the  more  important  series  are 
also  present  in  even  greater  intensity. 

Compton  and  Lilly,22  using  a  two  electrode  discharge  tube,  observed 
the  emission  of  the  arc  lines  of  helium,  Figure  10,  at  an  applied  potential 
of  25  to  35  volts.  The  spark  line  X  4686,  in  an  intense  arc,  was  observed 

M  Astrophys.  J.,  52,  pp.  1-7  (1920). 


136  ORIGIN  OF  SPECTRA 

at  a  minimum  potential  of  55  volts,  and  the  brightness  of  the  line  in- 
creased considerably  at  80  volts.  At  low  gas  pressure  and  current 
density  X  4686  was  not  perceptibly  excited  below  80  volts.  Under 
these  conditions  two  successive  collisions,  each  resulting  in  the  expulsion 
of  a  single  electron,  were  much  less  probable  than  a  single  80  volt  collision 
resulting  in  the  ejection  of  two  electrons. 

We  may  accordingly  conclude  that,  as  predicted  by  theory,  the  arc 
spectrum  of  helium  appears  at  25.5  volts,  the  ionization  potential,  and 
that  the  spark  lines  are  excited  at  54.2,  by  successive  impact,  and  at  79.7 
by  single  impact,  the  latter  values  corresponding  respectively  to  the 
work  required  to  eject  the  second  electron  after  the  first  is  removed,  and 
to  the  work  required  to  eject  both  electrons. 

Neon. — The  intricate  spectrum  of  neon  has  been  recently  correlated 
in  series  by  Paschen.23  It  is  characterized  by  sequences  of  the  form 
1  sx  —  mpv,  which  are  analogous  to  the  principal  series  of  the  metals, 
and  sequences  of  the  form  2  px  —  mdy  and  2  px  —  msy,  which  are  analo- 
gous to  the  subordinate  series  of  the  metals.  As  shown  in  Table  XIV 
there  are  two  resonance  potentials  and  three  ionization  potentials.  The 
latter  all  correspond  to  the  removal  of  a  single  electron  as  none  is  great 
enough  to  represent  successive  or  double  ionization.  Apparently  there 
are  three  slightly  different  energy  levels  in  which  the  outer  shell  of 
eight  electrons  are  distributed.  The  work  required  to  remove  a  second 
electron  from  the  neon  atom  after  the  first  has  been  ejected  cannot  be 
computed  nor  has  it  been  observed  experimentally. 

Horton  and  Davies24  have  observed  visually  the  stage  development  t 
in  the  neon  spectrum  at  the  three  ionization  potentials.     Their  con- 
clusions are  summarized  as  follows. 

First  ionization  16.7  volts.  No  visible  radiation.  Probably  all  the  radiation 

lies  in  the  extreme  ultra-violet. 

Second  ionization  20.0  volts.     Principal  series  lines  1  sx  —  mpv  begin,  to  appear. 

Third  ionization  22.8  volts.  Subordinate  series  lines  2  px  —  msu  and  2  px  — 

mdv  begin  to  appear. 

Apparently  the  phenomena  concerned  with  the  production  of  the 
arc  lines  of  neon  are  nearly  as  complicated  as  the  spectrum  itself.  The 
series  relations  in  the  arc  spectrum  may  be  intimately  connected  with 
those  in  the  L  series  of  the  x-radiation.25  Higher  types  of  spectra  which 
are  probably  enhanced  lines  may  be  obtained  in  a  spark  discharge  but 

I 

23  Ann.  Physik,  60,  p.  405  (1919);  63,  p.  201  (1920).  This  work  is  simply  summarized 
by  Fowler,  "Series  in  Line  Spectra,"  Chapter  XXI. 

**  Phil.  Mag.,  41,  pp.  921-40  (1921). 

25  Grotrian,  Z.  Physik,  8,  p.  116  (1921) ,  pointed  out  that  a  constant  frequency  difference 
between  arc  series  is  apparently  equal  to  the  extrapolated  L-doublet  separations. 


LINE  EMISSION  SPECTRA  137 

no  attempts  have  been  made  to  relate  these  to  the  velocity  loss  at  elec- 
tronic impact. 

FRANCK  AND  EINSPORN'S  OBSERVATIONS  ON  MERCURY 

In  order  to  discuss  the  recent  paper  of  Franck  and  Einsporn26  with 
sufficient  clarity,  it  appeared  advisable  to  consider  it  following  the 
foregoing  sections,  rather  than  to  have  introduced  it  earlier  in  the  treat- 
ment of  the  metals  of  Group  II.  These  investigators  obtained  evidence 
that  there  are  a  large  number  of  resonance  potentials  in  mercury  vapor 
and  that  lines  which  have  never  been  observed  should  be  present  in 
considerable  intensity. 

The  method27  employed  is  a  common  one  in  the  determination  of 
critical  potentials  (see  general  references  to  Chapter  III) .  The  electrons 
from  a  hot  wire  fall  through  a  definite  potential  and  collide  with  mercury 
atoms.  The  radiation,  emitted  by  an  atom  in  returning  to  or  toward 
the  normal  state  following  the  disturbance  produced  by  an  inelastic 
impact,  is  measured  by  its  photo-electric  effect  upon  an  auxiliary  electrode. 
The  photo-electric  current  leaving  this  electrode  is  plotted  as  a  function 
of  the  accelerating  voltage  of  the  impacting  electrons.  As  the  velocity, 
or  equivalent  voltage,  of  the  latter  is  gradually  increased,  an  increase 
in  the  radiation,  and  hence  in  the  observed  photo-electric  current, 
takes  place  at  each  critical  voltage  representing  an  inelastic  impact. 
Ordinarily  one  observes  an  increase  at  4.9  and  6.7  volts  corresponding 
to  the  well-known  resonance  potentials,  an  increase  at  10.3  corresponding 
to  ionization,  and  further  increases  at  combinations  of  these  values  such 
as  4.9  +  4.9  =  9.8;  4.9  +  6.7  =  11.6,  etc.  These  latter  represent 
successive  collisions  of  the  impacting  electrons. 

Franck  and  Einsporn's  curves,  which  were  obtained  with  the  greatest 
precision,  show  these,  and  many  more,  rapid  increases,  as  illustrated  by 
Figure  25.  In  Table  24  is  their  interpretation  of  the  observed  critical 
voltages.  Column  2  gives  the  observed  voltages  obtained  from  Figure 
25  and  similar  curves;  column  6  the  series  notation  of  the  radiation 
supposedly  producing  the  effects  observed;  and  the  last  column  gives  the 
values  computed  from  the  wave  numbers  by  Equation  (63).  Point 
No.  3  at  5.32  volts  corresponds  closely  to  measurements  of  McLennan 
and  Edwards,28  who  found  a  group  of  absorption  bands  in  mercury 

26  Z.  Physik,  2,  pp.  18-29  (1920). 

27  This  method,  which  permits  of  many  modifications,  was  devised  by  Davis  and  Goucher. 
Phys.  R.  10,  p.  101  (1917),  and  has  proved  to  be  one  of  the  most  important  means  for  the 
study  of  electron  impact. 

28 Phil.  Mag.,  30,  pp.  695-700  (1915). 


138 


ORIGIN  OF  SPECTRA 


vapor  between  X  2313  and  X  2338.  These  have  been  since  observed 
as  emission  bands  by  Grotrian.29  Probably  they  have  no  relation  to 
the  arc  spectrum  of  the  atom. 

Point  13  corresponds  to  a  displacement  of  the  valence  electron  to  the 
3  p2  orbit  and  point  14  to  a  displacement  to  either  3  P  or  3  d'.     Points 


i-Kurvel—        _ 
7      Kurvenll 

FIG.  25.     Photo-electric  current  versus  accelerating  voltage.     Franck  and  Einsporn's 
observations  with  mercury  vapor. 

16  and  17  may  be  due  to  displacements  to  higher  energy  levels  or  may  be 
the  result  of  two  successive  collisions,  each  displacing  an  electron  to  a  2  p 
orbit.  Besides  these  ejections  to  the  higher  mpz  and  mP  orbits  we  note 
displacements  to  2  ps  in  points  1,  15  and  possibly  16,  and  to  2  p\  in 
point  4.  Point  5  corresponds  to  the  removal  of  an  electron  from  the  2  p3 
orbit,  an  effect  of  cumulative  ionization  (Chapter  VI). 

2»  Z.  Physik,  5,  pp.  148-58  (1921). 


LINE  EMISSION  SPECTRA 


139 


TABLE  XXIV 
CRITICAL  VOLTAGES  IN  MERCURY  VAPOR;  FRANCK  AND  EINSPORN 


No. 
1 

Observed 
Volts 

Intensity  of 
Radiation 

X 

V 

Notation 

Computed 
Volts 

4.68 

Strong. 

2656 

37643 

IS  -2p, 

4.66 

2 

4.9 

Very  strong,  especially 
at  high  pressure. 

2537 

39413 

1  S  -  2  7)2 

4.86 

3 

5.32  « 

Weak. 

2313 
to  2338 

? 

5.3 

4 

5.47 

Weak;  at  medium  pres- 
sure strong. 

2271 

44041 

!S-2pi 

5.43 

5 

5.76 

Strong. 

2150 

46534 

2p3 

5.73 

6 

6.04 

Weak. 

? 

? 

? 

? 

7 

6.30 

Weak. 

? 

? 

? 

? 

8 

6.73 

Medium  strong. 

1849 

54066 

IS  -2P 

6.67 

. 
9 

7.12 

Strong  at  high  pres- 
sure;   weak  at  low 
pressure. 

? 

? 

? 

? 

10 

7.46 

Medium  strong. 

? 

? 

? 

? 

11 

7.73 

Medium  strong. 

1604 

62347 

IS  -Is 

7.69 

12 

8.35 

Weak. 

? 

? 

? 

? 

13 

8.64 

Weak. 

1436 

69658 

1  S  -  3  pz 

S.58 

14 

8.86 

Medium  strong. 

1403 
1400 

71291 
71393 

IS  -3P 

IS  -3d' 

8.79 
8.81 

15 

9.37 

Weak.' 

2656 
+  2656 

37643 

lS-2ps 

4.66  +  4.66 
=  9.32 

16 

9.60 

Weak. 

1308 
/    2556 

\+2537 

76463 
37643 
39413 

1  S  -  4  p2 
lS-2p, 
lS-2pz 

9.44 
4.66  +  4.86 
=  9.52 

17 

9.79 

Medium  strong. 

/    2537 
\+2537 
1269 

39413 
78810 

1  S  -  2  pz 
1  S  -  2  pz 
IS  -4P 

4.86  +  4.86 
=  9.72 
9.73 

18 

10.38 

Strong  at  low  pressure; 
weak  at  high  pressure. 

1188 

84178 

IS 

10.39 

140  ORIGIN  OF  SPECTRA 

There  is  nothing  contradictory  to  the  quantum  theory  in  the  presence 
of  inelastic  impacts  corresponding  to  1  S  —  2  pi  and  1  S  —  2  p3  or  to 
the  other  higher  mp  and  mP  terms.  Displacement  by  electronic  impact 
to  2  pi  or  2  pz  does  not  violate  the  principle  of  selection  even  when 
applied  to  so  restricted  a  theory  as  that  involved  by  Sommerf eld's 
internal  quantum  numbers,30  since  no  radiation  is  absorbed  or  emitted. 
However,  these  inelastic  collisions  were  observed  through  the  effect  of 
the  resulting  radiation.  Moreover,  if  an  electron  is  displaced  to  2  p3, 
the  next  orbit  to  1  S,  the  only  radiation  which  can  be  emitted  directly 
would  appear  to  be  1  S  —  2  p3.  Figure  25  shows  that  the  increase  in 
photo-electric  current,  which  is  proportional  to  the  intensity  4of  radiation, 
is  just  as  £reat  as  1  S  —  2  p3  (4.68  volts)  as  at  1  S  —  2  p2  (4.9  volts). 
Hence  this  unknown  line  X  2656  should  have  been  as  bright  as  the  well- 
known  line  X  2537.  It  is  scarcely  possible  that  if  such  a  line  existed 
it  would  not  have  been  observed  in  the  arc  spectrum  of  mercury,  which 
has  been  investigated  with  almost  all  possible  electron  velocities  in  this 
neighborhood.  A  similar  statement  applies  to  the  emission  of  1  S  — 
2  pi,  X  2271.  Possibly  the  inelastic  impacts  corresponding  to  these  lines 
exist  and  a  secondary  process  such  as  interatomic  collision  produces  a 
transfer  from  2  pi  or  2  p3  to  2  p2,  so  that  the  resulting  radiation  is  1  S  — 
2  p2.  Or  ejection  of  a  valence  electron  to  2  pi  and  2  p3  may  give  rise  to  a 
metastable  form  of  the  atom  which,  as  discussed  on  page  106,  possesses 
an  electron  affinity.  Molecules  may  be  then  formed  and  the  increase 
in  the  photo-electric  current  may  be  due  to  the  decomposition  of  these 
metastable  compounds  of  excited  and  normal  atoms. 

The  subject  is  by  no  means  closed.  If  further  work  more  clearly 
interprets  and  verifies  the  present  observations,  it  will  not  seriously 
conflict  with  the  principles  developed  in  this  book.  In  the  discussion 
of  resonance  potentials  where  we  have  made  the  statement  "only  two 
resonance  potentials  exist"  we  may  eventually  modify  this  to  read 
"only  two  important  or  pronounced  resonance  potentials  exist,"  admit- 
ting the  possibility  of  a  relatively  small  number  of  displacements  to 
higher  energy  levels.  Possibly  some  one  will  be  able  to  demonstrate 
that  lines  involving  higher  series  terms  are  emitted  as  a  result  of  elec- 
tronic impact  below  the  ionization  potential,  all  other  effects  of  cumula- 
tive ionization  being  subordinated.  At  the  present  time,  however, 
cumulative  ionization  and  the  few  high  velocity  electrons  always  present 
on  account  of  velocity  distribution  are  easily  sufficient  to  explain  all 
experiments  where  higher  series  terms  have  been  observed  spectroscopi- 
cally  below  the  ionization  potential. 


30  Sommerfeld,  "  Atombau,"  3d  Ed.,  Chapter  VI,  Section  5. 


LINE  EMISSION  SPECTRA  141 

QUANTITATIVE   SPECTROSCOPIC  ANALYSIS  IN   ITS   RELATION   TO   THE 

ORIGIN  OF  SPECTRA 

The  possibility  of  making  quantitative  analyses  by  spectroscopic 
means  has  been  agitated  for  a  century.  Some  success  has  been  attained 
in  the  past,  but  many  of  the  excellent  ideas  proposed  by  such  pioneers 
in  this  field  as  Lockyer,31  Hartley32  and  more  recently  by  de  Gramont33 
have  not  received  the  attention  they  merit.  For  several  years  Dr. 
W.  F.  Meggers  and  his  colleagues  have  been  engaged  in  a  systematic 
investigation  of  the  possibilities  of  the  method  and  have  clearly  demon- 
strated that  quantitative  analyses  can  be  made,  at  least  when  the 
material  sought  occurs  in  small  percentages,  of  the  order  of  one  per  cent 
and  less.34 

Several  experimental  facts  have  been  disclosed  in  this  work  which 
have  some  bearing  upon  the  subject  matter  of  this  book.  These  will 
be  considered  in  detail  in  a  future  paper  by  Dr.  Meggers,  who  has  placed 
the  preliminary  draft  of  his  manuscript  at  our  disposal.  The  empirically 
developed  subject  of  spectroscopic  analysis  has  to  deal  with  two  general 
phenomena:  (1)  the  "  long  lines"  of  Lockyer,  and  (2)  the  "raies  ultimes" 
of  de  Gramont  or  "  persistent"  lines  of  Hartley.  As  to  the  application 
of  these  phenomena  to  precise  analysis,  the  original  papers  of  Meggers 

j  must  be  consulted. 

Long  Lines.  —  If  the  entire  spark  or  arc  discharge  is  focused  on  the 

!;  slit  of  a  spectroscope  so  that  the  poles  appear  in  the  spectrum,  certain 

!  lines  of  an  impurity,  or  element  occurring  in  a  small  proportion,  appear 
long,  extending  from  pole  to  pole,  while  the  emission  of  other  spectral 
lines  is  confined  to  a  short  distance  in  the  immediate  neighborhood  of 
the  poles.  With  increasing  percentage  of  impurity  the  short  lines 

i   increase  in  length. 

Raies  Ultimes.  —  As  the  percentage  of  the  impurity  is  decreased, 
more  and  more  of  its  spectral  lines  disappear.  Certain  lines,  however, 
persist  even  when  the  impurity,  magnesium  for  example,  is  present  in 
the  extremely  minute  extent  of  one  part  in  1010.  The  persistent  lines, 
termed  by  de  Gramont,  "raies  ultimes,"  were  recognized  as  not  being 
necessarily  the  strong  or  intense  lines  of  the  ordinary  spectrum.  Further- 
more the  type  of  persistent  line  depends  upon  the  method  of  excitation. 
In  general  the  sensitive  lines  for  any  element  are  both  "long  lines" 
and  "raies  ultimes."  Discrepancies  arise  here  and  there  which  are 

«  Phil.  Trans.  163,  pp.  253,  639  (1873). 

32  Phil.  Trans.  175,  p.  325  (1884). 

33  Ann.  chim.  phys.  17,  pp.  437-77  (1909).     Compt.  rend.,  171,  p.  1106  (1920). 

34  Meggers,  Kiess  and  Stimson,  Bur.  Standards  Sci.  Paper  No.  444. 


142 


ORIGIN  OF  SPECTRA 


probably  attributable  to  the  fact  that  different  observers  have  investi- 
gated different  spectral  regions  and  certain  lines  have  been  thought  to 
have  been  the  long  lines  when  the  actual  long  lines  may  lie  in  a  spectral 
region  not  yet  investigated  carefully. 

Table  XXV  summarizes  Dr.  Megger's  correlation  of  the  raies  ultimes 
made  from  empirical  spectroscopic  observations.  It  may  be  found, 
especially  with  elements  of  other  than  Groups  I  and  II  of  the  periodic 
table,  that  as  the  spectral  range  investigated  is  extended,  even  more 
sensitive  lines  will  be  discovered  replacing  some  of  those  here  listed. 

TABLE  XXV 
RATES  ULTIMES  OF  THE  ELEMENTS 


Element 

Wave-length 
Angstrom  Units 

Intensity 

Notation 

Arc 

Spark 

Li   .    . 

6707.85 
6708.00 
4602.19 
5889.96 
5895.93 
3302.35 
7664.94 
7669.01 
4044.15 
4201.82 
4215.56 
4555.3 
4593.2 
3247.53 
3280.66 
2427.97 
2852.13 
2795.53 
4226.72 
3933.67 
4607.34 
4077.75 
5535.53 
4554.04 

3075.88 
2138.5 
3261.05 
2288.03 
2144.39 

20 

10 
50 
35 
30 
40 
30 
30 
30 
20 
20 
10 
100 
100 
10 
100 
20 
100 
50 
50 
20 
10 
10 
8 
4 

20 
10 
4 

20 

8 
20 
15 
20 
30 
20 
20 
20 
10 
10 
5 
30 
30 
20 
20 
50 
10 
100 
20 
40 
10 
20 
5 
4 
6 
10 
8 

Is  -  2  pi 
Is  -  2p2 
2p  -  4d 
l«-2p, 

1  s  —  2  p2 
Is  -  3pi 
Is  -  2Pl 
Is  -  2p2 
Is  -  3  pi 

1  8  -  3  pi 

1  s  -  3  p2 
1  s  -  3  pi 
Is  -  3p2 
Is  -  2  pi  . 
Is  -  2  pi 
1  s  -  2  pi 
IS  -  2P 
1  @  -  2  9i 
IS-  2P 
1@  -  2?i 
18-  2P 

1@   -  2?! 

IS  -  2P 

i3>-2fi 

1  S  -  2  pz 
1S-2P 
IS  -2pz 
1S-2P 

i  @  -  2  y$i 

Na 

K 

Rb  

Cs 

Cu  

Ag 

Au 

Mg.. 

Ca  

Sr  

Ba 

Zn  

d        

LINE  EMISSION  SPECTRA 

TABLE  XXV  —  Continued 
RAIES  ULTIMES  OF  THE  ELEMENTS 


143 


Element 

Wave-length 
Angstrom  Units 

Intensity 

Notation 

Arc 

Spark 

Hg 

2536.52 
3630.75 
3710.29 
3961.54 
4172.05 
4511.37 
5350.49 
2478.6 
2881.59 
3361.22 
3391.98 
3039.08 

2863.32 
3262.31 

4057.84 
4379.24 
4058.97 
3311.13 

2535.63 
2553.32 

2349.84 
2780.24 

10 
15 
30 
100 
30 
100 
100 
10 
30 
10 
10 
50 

20 
100 

100 

30 
50 
10 

10 
10 

10 
50 
100 
20 
20 
20 
30 
10 
15 
30 
20 
20 

15 
30 

50 
30 
10 
3 

5 
5 

10 
10 

1  S  -  2  p, 

2  pi  -  Is 
2  pi  -Is 

2Pl  -  Is 
2  Pi  -  Is 

Sc     

Yt 

Al 

Ga  

In 

Tl  

C 

Si 

Ti  

Zr  

Ge.   .. 

Sn  

Pb  

V.  .   . 

Cb  

Ta      . 

P  

As  

144 


ORIGIN  OF  SPECTRA 


TABLE  XXV  —  Continued 
RAIES  ULTIMES  OF  THE  ELEMENTS 


Element 

Wave-length 
Angstrom  Units 

Intensity 

Notation 

Arc 

Spark 

Sb  

2528.54 
3067.69 

3578.68 
3593.48 
4254.34 

3798.25 
3864.11 

4008.77 
2385.81 

2576.15 
4030.80 

2382.04 
2749.33 
3734.86 

2388.93 
2416.15 
3498.95 
3434.90 
3609.55 
3220.79 
3922.96 

10 
100 

30 
30 
50 

50 
50 

10 
3 

4 

100 

6 
4 
5 

2 
2 
50 
100 
100 
15 
10 

20 
30 

20 
20 
50 

20 
20 

10 
20 

30 
20 

10 
20 
10 

10 
15 
8 
10 
50 
-5 
15 

| 

Bi 

Cr 

Mo 

W             <•     ..   ; 

Te  

Mn     

Fe  At 

Co  :/:/. 

Ni 

Ru  

Rh 

Pd...  

Ir        .... 

Pt 

The  important  fact  which  Meggers  points  out  is  that  these  raies 
ultimes  are  almost  always  prominent  absorption  lines,  and  are  in  most 


144  A 


Ti 

-336  /  Tt 
^.3373  71 

\3363 


FIG.  26.     "Raies  ultimes"  for  several  elements. 


Pb-Al 


It  14    1  i     i 


FIG.  27.     An  example  of  "long"  and  "short"  lines. 


££ 


LINE  EMISSION  SPECTRA  145 

cases  the  first  lines  of  series  converging  at  1  S  or  Is,  where  the  spectrum 
of  the  element  concerned  has  been  correlated  in  series. 

That  is,  they  are  the  same  lines  which  determine  the  value  of  the 
resonance  potential,  or  which  appear  in  the  so-called  single-line  spectrum 
of  the  element  excited  below  the  ionization  potential.  We  accordingly 
have  another  method  for  locating  these  fundamentally  important  lines 
of  elements  for  which  the  series  relations  have  not  been  as  yet  established. 

If  the  spectra  are  excited  in  the  arc  the  raie  ultime  is  usually  the 
first  line  of  a  fundamentally  important  arc  series;  if  in  a  condensed 
spark,  usually  the  first  line  of  a  fundamentally  important  spark  series. 
This  fact  is  indicated  by  the  intensity  relations  given  in  Table  XXV. 

Figure  26  clearly  illustrates  these  conclusions.  The  material  in- 
vestigated was  carbon,  which  contained  small  amounts  of  a  large  number 
of  impurities  for  several  of  which  the  series  relations  are  known.  The 
outer  spectrogram  in  each  group  was  obtained  with  a  spark  discharge. 
The  magnesium  lines  appearing  are  the  pair  X  2795  —  2802,  1  <5  —  2  $ 
belonging  to  the  spark  spectrum  and  the  single  line  X  2852,  1  S  —  2  P, 
of  the  arc  spectrum,  the  former  being  present  in  the  greater  intensity. 
The  second  spectrogram  of  each  group  was  obtained  in  an  arc  discharge. 
Here  again  the  spark  pair  1  @  —  2  ^  is  present,  but  with  less  intensity 
than  the  arc  line  I  S  —  2  P.  The  inner  two  spectrograms  are  the 
ordinary  arc  and  spark  spectra  of  magnesium.  Certain  lines  which 
are  extremely  intense  in  these  spectra  are  readily  seen  to  be  absent  when 
the  amount  of  the  metal  is  decreased,  as  in  the  two  outer  spectrograms, 
so  that  the  phenomenon  is  not  at  all  a  matter  of  relative  intensity  with 
the  ordinarily  brighter  lines  persisting  when  the  dilution  increases. 
Similar  results  may  be  noted  with  calcium.  The  spark  pair  1  @  —  2  $ 
and  the  single  line  1  S  —  2  P  are  prominent.  Another  calcium  pair  is 
also  present,  belonging  to  a  subordinate  series  in  the  spark  spectrum. 
This  is  due  to  the  fact  that  more  calcium  is  present  than  is  necessary 
to  produce  the  raies  ultimes  alone.  At  percentages  of  Ca>  0.001  per 
cent,  this  second  pair  is  always  found,  while  for  lower  percentages  only 
the  raies  ultimes  are  present,  one  of  the  empirically  determined  and 
useful  facts  of  spectroscopic  analysis. 

In  addition  to  these  lines  we  note  the  appearance  of  the  first  pair  of 
the  principal  series  of  both  copper  and  silver.  By  analogy  one  would 
conclude  that  the  sensitive  lines  shown  for  the  other  impurities  should 
also  belong  to  fundamentally  important  series  of  a  similar  type,  but 
unfortunately  these  are  unknown. 

Figure  27  shows  some  long  and  short  lines  in  the  spark  spectra  of  two 


146  ORIGIN  OF  SPECTRA 

different  alloys.  For  example,  the  three  aluminum  lines  X  3587,  3602 
and  3613  in  the  upper  spectrogram  appear  at  the  electrodes  only,  while 
the  lines  X  3944,  3962  are  long  lines  extending  throughout  the  space 
between  the  electrodes.  The  latter  constitute  the  first  pair  of  the  2d 
Subordinate  series  while  the  classification  of  the  former  is  unknown.  In 
the  lower  spectrogram  one  may  readily  note  the  difference  in  appearance 
of  the  lead  lines  X  4019,  4168  and  the  lines  X  4245,  4387,  the  latter  being 
"  short"  lines,  as  is  evidenced  by  the  very  much  higher  intensity  at  the 
poles. 

This  figure  is  given  simply  to  indicate  the  general  appearance  of 
long  and  short  lines.  Unfortunately  photographs,  suitable  for  reproduc- 
tion, are  not  available  to  the  authors  to  clearly  illustrate  the  present 
discussion  of  the  physical  behavior  of  long  lines.  Most  of  the  work  in 
this  field  has  been  done  either  with  elements  for  which  the  series  rela- 
tions are  unknown  or  has  embraced  a  too  limited  portion  of  the  spectrum. 

A  careful  study  of  Table  XXV  shows  that  some  fundamentally 
important  series  lines  do  not  appear  to  be  raies  ultimes,  for  example 
the  line  1  S  —  2  p2,  X  4571  of  magnesium.  Why  this  should  be  true  is 
not  apparent.  In  fact  the  true  physical  significance  of  all  the  foregoing 
phenomena  is  not  evident,  and  will  involve  further  study. 

We  probably  have  in  the  arc  or  spark  a  distribution  of  potential 
in  which  most  of  the  gradient  is  confined  to  the  anode  and  cathode,  with 
very  little  drop  in  the  arc  itself.  Consequently  the  electrons,  except 
near  the  electrodes,  may  not  accumulate  velocities  exceeding  the  reso- 
nance potentials  of  the  impurities.  Accordingly  lines  of  the  arc  and 
spark  spectra  other  than  those  of  the  so-called  fundamental  type  can 
not  be  excited  throughout  the  central  portion  of  the  arc.  Furthermore, 
the  excitation  of  these  fundamentally  important  lines  may  give  rise  to 
resonance  radiation  which  through  absorption  and  re-emission  becomes 
uniformly  distributed  throughout  the  volume  of  vapor,  thus  accentuating 
the  presence  of  the  "long  lines." 

We  are  able  to  offer  only  a  suggestion  in  regard  to  the  origin  of  the 
raies  ultimes.  Suppose  Zn  occurs  as  an  impurity  in  Mg  to  the  extent  of 
1  Zn  atom  for  every  100,000  Mg  atoms.  The  arc  spectrum  will  show 
all  arc  lines  of  Mg  and  the  Zn  arc  lines  1  S  —  2  p2  and  1  S  —  2  P,  the 
raies  ultimes  of  Zn.  We  may  assume  that  since  the  electrons  emitted 
by  the  cathode  can  not  be  discriminatory,  the  probability  of  collision 
with  a  metal  atom  is  proportional  to  its  concentration. 

Hence  in  general  an  arc  line  of  Zn  will  be  1/100,000  as  intense35  as  th< 

35  Neglecting  modifying  factors  such  as  differences  in  ionization  potential,  cross 
of  atom,  etc. 


LINE  EMISSION  SPECTRA 


147 


corresponding  line  in  Mg,  and  would  certainly  not  be  observed.  But 
in  the  case  of  resonance  lines  (lines  absorbed  and  re-emitted  by  the 
surrounding  vapor)  the  above  reasoning  does  not  hold.  The  absorption 
factor  increases  with  the  concentration.  Hence  only  for  extremely 
rare  vapors  is  the  intensity  of  emission  proportional  to  the  concentra- 
tion, and  with  increasing  partial  pressure  of  the  absorbing  atoms  a  stage 
is  soon  reached  where  the  increase  in  intensity  becomes  relatively  small. 
The  problem  of  the  arc  discharge  is  so  complicated  that  a  mathematical 
treatment  of  the  subject  is  out  of  the  question,  but  in  the  much  simpler 
case  of  flame  spectra  (Chapter  VII)  the  emission  of  resonance  lines  under 
thermal  excitation  is  treated  in  some  detail.  The  theory  is  applied 
only  to  dilute  vapors,  but  the  equations  used  indicate  the  manner  in 
which  the  absorption  factor  would  enter  with  increased  concentration. 
These  considerations  apply  equally  well  to  either  electrical  or  thermal 
excitation. 

The  quantitative  results  for  extremely  dilute  vapors  in  flames  indi- 
cate that  in  an  arc  the  thermal  excitation  alone  would  suffice  to  explain 
the  appearance  of  the  raies  ultimes  of  minute  traces  of  an  element. 
This  fact  together  with  the  above  mentioned  absorption  factor  gives 
at  least  a  qualitative  explanation  for  the  appearance  of  resonance  lines 
of  an  impurity,  with  an  intensity  comparable  to  that  of  the  arc  lines 
of  a  concentrated  vapor.  The  fact  that  some  of  the  raies  ultimes  listed 
in  Table  XXV  are  subordinate  series  lines  is  not  necessarily  in  con- 
tradiction to  the  above  theory.  Resonance  lines  of  normal  atoms  are 
indeed  principal  series  lines,  but  if  the  resonance  potential  is  very  low, 

ly  of  the  atoms  in  an  arc  will  be  in  the  2  p  state.  These  excited 
atoms  will  absorb  and  re-emit  subordinate  series  lines.  For  such  atoms, 
lines  of  subordinate  series  will  possess  the  characteristics  of  "  raies 
ultimes"  and  "long  lines.7' 


Chapter  VI 
Cumulative  lonization 

Cumulative  ionization  denotes  the  process  whereby  atoms  may  be 
ionized  by  successive  stages  of  excitation.  (1)  A  valence  electron  may 
be  ejected  to  an  outer  orbit  such  as  2  pz  by  electronic  collision  and  the 
excited  atom  thus  formed  may  collide  with  a  second  electron  having  a 
velocity  sufficient  to  completely  eject  the  valence  electron.  This 
process  is  known  as  ionization  by  successive  impact.  (2)  A  valence 
electron  may  be  ejected  to  an  outer  orbit  by  absorption  of  radiation, 
and  the  excited  atom  thus  formed  may  collide  with  an  electron  having  a 
velocity  sufficient  to  complete  the  process  of  ionization.  Compton 
designates  this  as  photo-impact  ionization.  (3)  The  valence  electron 
may  be  ejected  to  an  outer  orbit  by  absorption  of  radiation,  and  the 
process  of  line  absorption  continued  until  the  atom  is  ionized.  This 
may  be  called  ionization  by  successive  photo-electric  action.  These  pro- 
cesses may  be  of  course  jointly  involved  with  several  absorptions  of 
radiation  followed  by  an  electronic  impact. 

K.  T.  Compton1  has  made  a  mathematical  analysis  of  the  processes 
(1)  and  (2) .  He  has  derived  an  expression,  in  terms  of  measurable  quan- 
tities, which  gives  the  fractional  number  of  gas  atoms  at  any  instant  in 
the  excited  state,  and  hence  in  a  condition  for  ionization  by  electronic 
impact  below  the  ionization  potential;  (1)  as  a  result  of  electronic 
collision  and  (2)  as  a  result  of  absorption  of  resonance  radiation  from 
neighboring  atoms  which  have  been  previously  excited  by  electronic 
impact.  Necessarily  rather  questionable  assumptions  must  be  made 
in  order  to  simplify  the  analysis,  but  the  results  are  probably  somewhere 
near  the  correct  order  of  magnitude,  which  is  sufficient  for  the  present. 
The  following  outlines  Compton's  method  in  the  treatment  of  the 
problem. 

Figure  28  represents  a  cylindrical,  two-electrode  discharge  tube, 
filled  with  vapor,  in  which  A  is  the  anode  and  C  the  hot  wire  cathode, 
mounted  concentrically.  If  the  accelerating  field  V  is  less  than  the 

i  Phys.  B.,  20  (1922). 

148 


CUMULATIVE  IONIZATION 


149 


ionization  potential  Tr«  but  greater  than  the  resonance  potential  Vr, 
inelastic  collisions  will  occur  resulting  in  excitation  of  the  atoms  and 
subsequent  emission  of  radiation.  For  a  given  applied  potential  differ- 
ence V,  an  individual  electron  will  attain  a  velocity  Vr  at  a  certain 
distance  from  the  cathode.  However,  since  an  impact  with  an  atom 
may  not  occur  at  precisely  the  instant  the  electron  attains  this  velocity, 
and  for  another  reason  explained  later,  we  shall  have  for  all  the  emitted 
electrons  a  region  of  effective  collision,  a  small  volume  inclosed  by  two 
concentric  cylindrical  surfaces,  represented  by  the  shaded  portion  of  the 
diagram. 


FIG.  28.     Cross  section  of  discharge  tube. 

EXCITATION  BY  ELECTRONIC  IMPACT 

Let  the  n  electrons  emitted  per  second  by  the  cathode  collide  effectu- 
ally in  the  shaded  space  of  Figure  28.  Excited  atoms  are  accordingly 
produced  which  remain  in  the  excited  state  for  an  average  time  interval 
T  second.  If  P  denotes  the  fractional  number  of  atoms  which  at  any 
instant,  for  any  reason  whatever,  are  in  the  excited  condition,  then 
n(l—P)  atoms  are  excited  per  second  by  electronic  impact,  and  the  aggre- 
gate time  of  excitation  of  all  the  atoms  is  n  (I  —  P)  T.  This  divided 
by  the  total  number  of  atoms  in  the  shaded  volume  gives  the  fractional 


150  ORIGIN  OF  SPECTRA 

number  of  atoms  which  at  any  instant  are  in  the  excited  state  as  the 
direct  result  of  electronic  impact.  Calling  this  fraction  Pt,  we  have 

„        n(l  —  P)r         nr 

Pt  =    —NT    =^'  approximately 

where  p  is  the  gas  pressure  in  mm  Hg,  N  is  the  number  of  atoms  per 
cm3  at  a  pressure  of  1  mm  Hg  and  v  is  the  volume  of  the  shaded  cylindri- 
cal shell  within  which  the  effective  impacts  occur.  If  /  is  the  length  of 
this  volume  and  d  its  width,  evidently 

v  =  2  7r(6  +  c)/5.  (94) 

From  the  distribution  of  potential  in  a  concentric  arrangement 
such  as  here  considered  we  find 

V~Vri  a 

b  +  c  =  at~    v    ln*,  (95) 

where  a  and  c  are  the  respective  radii  of  the  anode  and  cathode.  The 
calculation  of  d  is  more  difficult,  for  it  depends  on  the  average  distance 
which  the  electrons  move  beyond  the  point  at  which  they  have  acquired 
the  velocity  VT  before  making  an  effective  impact,  and  also  on  the 
distribution  of  velocities  of  electrons  which  causes  them  to  gain  the 
critical  velocity  at  different  distances  from  the  cathode.  Compton 
derives  the  formula 

5=  A/I  -+^(6  +  c)Zn-,  (96) 

in  which  Y    8  p      eV  c  ' 

I      =  mean  free  path  of  an  electron  at  a  pressure  of  1  mm  Hg 

aT  =  average  kinetic  energy  of  an  atom  at  the  cathode  temperature  T. 

We  accordingly  obtain  from  Equations  (93)  ,  (94)  and  (95) 


2  ir(b  +  c)f5Np  ' 

where  d  may  be  computed  from  Equation  (96).  This  gives  the  frac- 
tional number  of  atoms  which  at  any  instant  are  in  the  excited  state  as 
the  direct  result  of  impact. 

EXCITATION  BY  ABSORPTION  OF  RADIATION 

Impacts  in  the  shaded  layer  produce  radiation  which  is  absorbed 
and  re-emitted  by  atom  after  atom  before  escaping  from  the  vapor  so 
that,  as  a  result  of  the  activation  of  a  single  atom  by  direct  impact, 
many  other  atoms  are  successively  activated  through  absorption  of  the 
emitted  radiation.  Thus  at  any  instant  the  fractional  number  Pr  of 
atoms  in  the  excited  state  as  a  result  of  absorption  of  radiation  should 
be  greater  than  Pi  if  much  absorption  occurs. 


CUMULATIVE  IONIZATION  151 

The  quanta  of  radiation  are  passed  on  from  atom  to  atom,  diffusing 
through  the  vapor  in  all  directions  in  a  manner  analogous  to  the  diffusion 
of  a  foreign  gas,  and  accordingly  the  same  mathematical  procedure 
may  be  employed  in  the  treatment  of  the  two  problems.  A  beam  of  light 
passing  through  an  absorbing  or  scattering  medium  decreases  in  intensity 
according  to  the  law 

I  =  I0e-*x,  (98) 

where  k  is  the  absorption  coefficient.     A  stream  of  particles  passing 
through  a  gas  is  reduced  by  collisions  or  scattering  according  to  the  law 

n  =  nQe-x/l,  (99) 

where  I  is  the  mean  free  path. 

We  may  define  p  as  the  reciprocal  of  the  absorption  coefficient  fc, 
i.e.  as  the  distance  in  which  the  intensity  of  a  beam  of  monochromatic 
radiation  through  a  vapor  at  1  mm  pressure  decreases  to  1/6  of  its  initial 
value.  By  analogy  to  Equation  (99),  this  is  the  mean  free  path  of  a 
quantum  in  a  gas  at  1  mm  pressure,  and  the  mean  free  path  at  p  mm 
pressure  is  accordingly  p/p.  Although  in  our  particular  problem  some 
of  the  atoms  are  excited  and  hence  are  incapable  of  absorbing  or  scatter- 
ing resonance  radiation,  the  fractional  number  in  this  condition  is  too 
small  to  alter  materially  the  value  of  the  mean  free  path  p/p  strictly 
applicable  to  normal  atoms.  Accordingly  the  average  speed  c  of  the 
radiation  is  equal  to  the  distance  p/p  divided  by  the  time  r  in  which  an 
atom  on  the  average  remains  in  the  excited  condition.  We  may  there- 
fore apply  the  diffusion  equation: 


where  N'  is  the  number  of  excited  atoms  per  cm3  at  any  point  at  any 
instant  in  the  vapor  of  pressure  p,  R  is  the  net  rate  at  which  atoms  are 
excited  by  direct  electron  collision  and  t\  is  the  outward  normal  to  the 
closed  surface  over  which  the  surface  integral  and  within  which  the 
volume  integral  are  taken.  For  details  as  to  the  application  of  Equation 
(100)  in  the  solution  of  our  problem,  the  original  paper  must  be  consulted. 
Compton  shows  that  with  reasonable  assumptions  and  for  V  not  very 
much  greater  than  VT  the  following  expression  is  derivable. 


Since  there  are  Np  atoms,  N7  of  which  at  any  instant  are  in  the  excited 
state,  we  obtain 

-T1       a. 


Np       2  irfNp2 


152  ORIGIN  OF  SPECTRA 


NUMEKICAL  MAGNITUDES 

The  relative  importance  of  Pr  and  P(  is  obtained  on   dividing 
Equation  (102)  by  Equation  (97)  as  follows. 


Pr  _  3p«(6  +  c)g  V-Vr  ,    a 
Pi"        ~^~         ~V~lnc' 

As  mentioned  on  page  89  Wood  found  that  the  intensity  of  the 
resonance  radiation  of  mercury  X  2537  was  reduced  to  \  its  value  in 
traversing  a  distance  of  0.5  cm  through  mercury  vapor  at  a  pressure 
0.001  mm  Hg.  This  datum  in  the  above  defined  units  makes  p  =  0.0007. 
Reasonable  constants  for  the  dimensions  of  the  discharge  tube  are: 
a  =  0.5  cm;  c  =  0.025  cm;  /  =  1  cm.  For  mercury  Vr  =  4.9  volts.  Let 
the  total  applied  potential  exceed  this  by  one  volt,  i.e.  V  =  5.9. 

On  carrying  through  the  computations  involved  in  Equation  (96) 
it  is  found  that  5  is  roughly  constant,  averaging  about  8  =  .04  for  a  wide 
range  of  pressure  and  temperature  of  the  cathode.  We  thus  obtain 
from  (103)  ^ 

^  =  40,000  p2 
*  i 

=  40,000  at  1  mm  pressure 

=  4,000,000  at  10  mm  pressure. 

Now  the  probability  of  an  electron  colliding  with  an  excited  atom 
and  of  ionizing  below  the  ionization  potential  is  proportional  to  Pr  + 
P«.  It  is  therefore  evident  that  ionization  by  photo-impact  is  relatively 
of  far  greater  importance  than  ionization  by  successive  impact  es- 
pecially at  the  higher  vapor  pressures. 

We  shall  now  consider  Equation  (102)  to  determine  whether  ioniza- 
tion by  photo-impact  is,  in  itself,  an  important  factor  in  arc  phenomena. 
One  serious  difficulty  here  is  our  inadequate  knowledge  of  the  quantity  r 
an  estimate  of  which  was  stated  in  Chapter  IV  to  be  10~8  seconds. 
Using  this  value  and  the  data  given  above  we  accordingly  obtain  from 
(102) 

Pr= 


The  number  of  electrons  n  leaving  the  cathode  in  the  absence  of  any 
ionization  is  limited  by  the  space  charge  and  may  be  computed  from  the 
Langmuir  formula  n  =  1.8-1014  V*  =  2.5-1015  in  which  the  constants 
of  the  particular  apparatus  have  been  substituted.  This  relation  is 
strictly  true  only  in  vacuo,  and  actually,  the  current  will  be  somewhat 


CUMULATIVE  IONIZATION  153 

less  since  the  presence  of  the  gas  around  the  cathode  reduces  the  rate  of 
escape  of  electrons.  We  finally  obtain  for  PT  in  this  favorable  case: 

PT  =  2.5-10~4p, 

or  at  a  pressure  of  2  mm  Hg,  Pr  =  5-lQ-4.  If  r  =  6-10-7  (cf.  Stark2 
for  work  with  helium)  this  value  should  be  increased  by  a  factor  of  60. 

ARCS   BELOW   THE   IONIZATION   POTENTIAL 

It  is  a  well-known  observation  that  arcs  in  vapors  may  be  struck 
when  the  applied  potential  is  only  slightly  greater  than  the  resonance 
potential.  We  shall  show  that  the  computed  value  of  Pr  is  sufficient  to 
explain  this  phenomenon.  If  Pr  represents  the  fractional  number  of 
excited  atoms  at  any  instant  and  n  the  number  of  electrons  emitted 
per -second  by  the  cathode  in  the  absence  of  ionization,  the  number  of 
electronic  collisions  per  second  in  the  shaded  space  of  Figure  28,  which 
occur  with  excited  atoms,  is  nPr.  If  V  >  (Vt  —  Vr),  these  collisions 
result  in  the  production  of  nPT  ions  per  second. 

The  ionization  of  an  atom  increases  the  current  in  two  ways,  first  by 
releasing  an  electron  and  second  by  creating  a  slowly  moving  positive 
ion  and  thus  neutralizing  a  part  of  the  negative  space  charge  which 
limits  the  thermionic  emission.  The  positive  ion  remains  in  the  field 
4  V3680  M  times  as  long  as  an  electron,  where  M  is  the  atomic  weight 
of  the  atom-ion.  One  ion  accordingly  neutralizes  the  effect  on  the  space 
charge  of  4  V3680  M  electrons.  This  permits  the  emission  of  more 
electrons  from  the  cathode,  some  of  which  in  turn  collide  with  excited 
atoms,  produce  more  ions  and  release  more  electrons.  Compton  shows 
that  under  these  conditions  the  total  number  n'  of  electrons  leaving  the 
cathode  per  second  is 

n'  =  J1  ,  (104) 

1  -  4  \/3680  M  Pr 

where  Pr  as  before  is  the  fractional  number  of  atoms  which  at  any 
instant  are  excited  by  the  radiation  produced  by  an  emission  of  n  elec- 
trons per  second,  that  is,  in  the  absence  of  any  cumulative  ionization. 
As  Pr  is  increased,  the  ratio  n'/n  increases  more  and  more  rapidly, 
becoming  infinite  at  Pr  =  1/4  A/3680  M  were  the  emission  not  limited 
physically  by  the  value  corresponding  to  the  saturation  thermionic 
current  at  the  temperature  of  the  cathode.  With  mercury  such  a 
condition  is  reached  when  Pr  =  2.91  •  10"4,  whereas  our  computed  value 

2  Ann.  Physik,  49,  p.  731  (1916). 


154  ORIGIN  OF  SPECTRA 

of  PT  at  2  mm  pressure  was  nearly  double  this.  The  value  Pr  =  5- 10"4 
was  computed,  however,  with  very  favorable  assumptions.  If  Pr  is 
only  2.9 -10-4  we  find  by  Equation  (104)  that  n'/n  =  1000.  Observed 
values  range  roughly  from  2  to  100.  The  observed  rapid  increase  in 
current  just  before  the  arc  strikes  is  accordingly  amply  explained  by 
cumulative  ionization  of  the  photo-impact  type. 

This  rapid  increase  in  ionization  and  resulting  production  of  ions 
thus  neutralizes  the  space  charge,  and  as  the  electron  emission  is  limited 
by  its  saturation  value,  finally  develops  a  positive  space  charge.  When 
the  space  charge  becomes  positive,  the  potential  drop  is  concentrated 
at  the  cathode  so  that  the  electrons  attain  their  critical  speed  within  a 
short  distance  from  the  cathode.  This  concentration  of  the  region  of 
effective  impacts  tends  further  to  increase  the  probability  of  cumulative 
ionization.  At  the  same  time  the  temperature  of  the  cathode  is  raised 
by  the  bombardment  of  the  positive  ions3  which  again  increases  n  and 
Pr.  We  now  have  a  condition  of  instability:  the  arc  strikes,  and  the 
complete  arc  spectrum  of  the  vapor  may  be  produced  below  the  ioniza 
tion  potential,  at  a  potential  V  =  Vt  —  Vr. 

On  account  of  the  concentration  of  the  potential  gradient  near  the 
cathode  as  soon  as  a  large  number  of  ions  are  formed,  electrons  more 
nearly  attain  the  full  velocity  of  the  impressed  field  before  the  first 
collisions  with  atoms  occur.  Somewhat  the  same  distribution  of  po- 
tential is  produced  as  that  obtained  in  a  more  controllable  manner  by 
the  use  of  an  auxiliary  electrode,  as  shown  in  Figure  22.  Hence  as  the 
applied  voltage  is  increased  to  V*  corresponding  to  1  ©  for  the  alkali 
earths,  enhanced  lines  may  appear.  The  favorable  condition  for  excita- 
tion of  enhanced  lines  in  a  two  electrode  arc  is  high  current  density. 
The  high  current  involves  a  large  number  of  ions  which  neutralize  the 
negative  space  charge  and  increase  the  potential  gradient  at  the  cathode. 
This  well-known  method  for  exciting  enhanced  lines  has  led  to  some 
misapprehension  as  to  their  origin.  Many  investigators  have  con- 
sidered the  purely  incidental  effect  of  high  current  to  be  the  prime  factor 
in  the  physical  process  of  the  excitation. 

IONIZATION  BY  SUCCESSIVE  PHOTO-ELECTRIC  ACTION 

The  mathematical  analysis  of  this  process  is  so  involved  that  the 
results  are  not  readily  interpreted.  However,  there  is  no  doubt  from 
the  experimental  standpoint  that  the  phenomenon  is  of  importance. 
We  may  have  several  absorptions  of  radiation  followed  by  an  electronic 

3  The  beginner  usually  burns  up  the  cathode  and  an  ammeter  at  this  stage. 


CUMULATIVE  IONIZATION  155 

impact  which  completes  the  ionization  process,  or  without  any  electronic 
impact  whatever  most  of  the  arc  lines  may  be  produced,  under  proper 
experimental  conditions,  showing  that  the  valence  electron  may  be 
driven  to  a  remote  outer  orbit  if  not  completely  ejected. 

A  notable  example  of  the  latter  process  is  the  experiment  of  Fucht- 
bauer4  who  observed  the  emission  of  the  mercury  arc  lines  as  a  result 
solely  of  the  absorption  of  radiation.  This  was  considered  in  detail  in 
Chapter  IV,  the  last  half  of  which  is  intimately  concerned  with  the 
experimental  verifications  of  this  theory  of  successive  photo-electric 
action.  In  the  case  of  sodium,  for  example,  the  atom  absorbs  a  quantum 
of  D-radiation  resulting  in  the  ejection  of  a  valence  electron  to  the  2  p 
orbit.  Before  the  time  interval  r  elapses,  a  second  quantum  may  be 
absorbed.  This  may  have  a  frequency  corresponding  to  any  term  in 
any  series  converging  at  2  p.  For  example  it  may  be  the  first  term  of  the 
first  subordinate  series  2  p  —  3  d,  in  which  case  the  valence  electron  is 
ejected  to  the  3  d  orbit,  et  cetera.  At  any  stage  in  this  process  of  absorp- 
tion, in  an  arc,  an  electronic  impact  may  occur,  assisting  in  the  process 
of  the  ejection  of  the  valence  electron. 

FURTHER  CONCLUSIONS 

We  have  noted  above  that  an  arc  may  be  struck  below  the  ionization 
potential  if  the  applied  voltage  V>  (Vt  —  Vr).  With  mercury  Vt  — 
VT  =  10.3  —  4.9  =  5.4  volts.  The  phenomenon  of  absorption,  how- 
ever, under  suitable  experimental  conditions,  reduces  this  minimum 
voltage  to  Vr  or  4.9  volts.  The  4.9  volt  impacts,  indirectly  through 
the  absorption  of  the  resulting  radiation,  maintain  a  large  number  of 
atoms  with  the  valence  electron  in  the  2  p2  orbit.  A  4.9  volt  impact 
with  such  an  excited  atom  is  capable  of  ejecting  an  electron  to  the  3  s 
or  4  d  orbits.  The  radiation  subsequently  resulting  from  this  ejection 
will  maintain  a  proportion  of  excited  atoms  with  electrons  in  these  higher 
energy  levels.  A  collision  of  4.9  volts  with  such  atoms  is  more  than 
sufficient  to  ionize.  Accordingly  arcs  may  be  struck  at  the  lowest 
resonance  potential  of  the  vapor. 

A  final  observation  is  the  well-known  fact  that  arcs  once  struck  will 
continue  to  operate  even  when  the  applied  voltage  is  less  than  the 
resonance  potential.  The  most  important  factor  here,  in  addition  to  the 
points  brought  out  in  the  foregoing  discussion,  is  the  photo-electric  effect 
of  the  resonance  radiation  on  the  cathode.  Van  der  Bijl5  mentions  that 

4  Physik.  Z.,  21,  pp.  635-8  (1920). 
s  Phys.  R.,  10,  p.  546  (1917). 


156  ORIGIN  OF  SPECTRA 

X  2537  of  mercury  should  liberate  photo-electrons  from  a  calcium-coated 
cathode  with  an  initial  velocity  of  1.5  volts,  so  that  an  arc  in  mercury 
once  started,  might  be  maintained  at  4.9  —  1.5  =  3.4  volts.  Radiation 
of  wave-length  as  short  as  X  1188  is  present  in  the  arc  so  that  some 
photo-electrons  of  still  higher  velocity  are  liberated.  Still  further,  a 
few  high  velocity  electrons  are  emitted  in  accordance  with  the  Max- 
wellian  distribution  of  velocities,  as  shown  by  Equation  (86).  And 
finally  the  ions  created,  in  falling  into  the  cathode,  may  liberate  electrons 
of  considerable  speed.  All  of  these  factors  must  be  considered  in  inter- 
preting the  action  of  certain  rectifiers  which  may  be  operated  at  astonish- 
ingly low  voltages.  In  this  case  we  have  in  addition  the  favorable  fact 
that  the  maximum  voltage  is  greater  than  the  measured  root  mean 
square  voltage.  However,  a  discussion  of  rectifiers  is  beyond  the  scope 
of  this  book. 

The  conclusion  to  be  drawn  from  the  foregoing  considerations  is  that 
the  phenomenon  of  absorption  of  radiation  plays  an  important  role  in 
arc  characteristics  and  emission  of  radiation.  Cumulative  ionization 
of  the  photo-impact  type  becomes  a  controlling  factor  with  high  elec- 
tronic emission  and  vapor  pressure.  It  is  possible  that  ionization  by 
successive  impact  is  of  some  importance  at  very  low  pressure,  but  in 
general,  compared  to  the  effect  of  absorption  of  radiation,  its  action  is 
insignificant. 

This  latter  statement  of  course  applies  only  to  simple  ionization. 
Successive  or  multiple  ionization  is  readily  produced  by  successive  impact 
as  shown  in  the  appearance  of  the  enhanced  spectrum  of  magnesium  at 
14.97  volts  (cf.  discussion  of  Figure  23).  The  probability  of  multiple 
ionization  by  successive  impact  depends  upon  the  time  of  recombination 
for  the  ion  formed  at  the  first  impact.  This  time  interval,  which 
corresponds  to  r,  may  be  relatively  very  large,  depending  upon  the 
probability  of  a  collision  between  an  ion  and  an  electron  of  small  kinetic 
energy.  It  should  be  accordingly  a  function  of  the  design  of  any  particu- 
lar apparatus.  Child6  has  made  extensive  experiments  with  a  mercury 
arc  excited  by  a  sixty  cycle  current.  By  examining  the  intensity  of 
the  arc  lines  at  various  phases  of  the  cycle  he  found  that  the  minimum 
intensity  lagged  behind  the  time  of  zero  current  and  voltage  by  an 
interval  of  1/1800  second.  Experiments  of  other  observers  also  indicate 
that  we  are  here  dealing  with  a  time  interval  of  an  entirety  different  order 
of  magnitude  than  10"8  seconds,  the  value  of  r  for  a  neutral  atom. 

•  Phys.  R.,  9,  pp.  1-14  (1917). 


Chapter  VII 
Thermal  Excitation 

THERMODYNAMIC  CONSIDERATIONS 

The  absolute  entropy  of  a  mol  of  perfect  gas  is  given  by  the  following 
formula: 

S  =  |  R  InT  -  R  Inp  +  f  R  InM  +  Si,  (105) 

where  M  is  the  molecular  weight,  R  =  1.985  cal.  deg'1,  p  throughout 
this  chapter  except  where  otherwise  noted,  the  pressure  expressed  in 
atmospheres,  T  the  absolute  temperature,  and  S\  =  —  3.2  cal.  deg~l. 
Evidence  for  the  value  of  S\  and  its  constancy  with  various  mona- 
tomic  gases  has  been  discussed  by  Tolman1  and  others. 

It  has  been  recognized  for  some  time  in  mathematical  treatments 
of  thermionic  emission,  thermoelectricity,  contact  potential,  etc.,  that 
electrons  may  be  considered  as  a  gas,  the  laws  of  which  they  obey  in 
detail,  one  example  being  the  Maxwellian  distribution  of  velocities. 
The  pressure  of  this  gas  in  any  laboratory  experiment  is  exceedingly 
small,  of  the  maximum  order  of  magnitude  10"8  atmospheres,  so  that 
considering  an  electronic  atmosphere  as  a  perfect  gas  should  be  open  to 
no  objection. 

From  data  on  the  thermionic  emission  of  tungsten,  tantalum  and 
molybdenum,  and  measurements  of  the  cooling  of  the  filament,  due  to 
the  latent  heat  of  vaporization  of  the  electrons,  Tolman2  shows  that 
the  entropy  of  electron  gas  is  given  by  Equation  (105)  where  S\  has 
the  same  value  as  for  a  perfect  monatomic  gas.  The  value  of  M  for 
electrons  is  of  course  expressed  on  the  scale  M  =  1.008  for  the  hydro- 
gen atom,  whence  Me  =  5.46- 10~4. 


1  J.  Am.  Chem.  Soc.,  42,  pp.  1185-93  (1920). 

2  J.  Am.  Chem.  Soc.,  43,  pp.  1592-1601  (1921). 

157 


158  ORIGIN  OF  SPECTRA 

Accordingly  if  it  is  possible  to  determine  the  absolute  entropy  of 
both  gases  and  electrons  by  Equation  (105),  we  may  predict  from 
thermodynamic  considerations  the  extent  to  which  a  reaction  such  as 
ionization  may  proceed  at  any  desired  temperature.  Tolman's3  deriva- 
tion of  the  react  ion-isochore  is  given  in  the  following  paragraphs. 

Consider  a  reversible  reaction  of  the  type 

Ca  =  Ca+  +  E-  -  J,  (106) 

where  Ca,  Ca+  and  E~  are  respectively  gram  mols  of  neutral  calcium 
atoms,  simply  charged  positive  calcium  ions,  and  electrons,  and  J  is  the 
work,  expressed  in  calories,  required  to  ionize  one  mol  of  calcium  atoms. 
If  /  is  the  value  of  the  faraday.  Vt  the  ionization  potential  in  volts,  and 
j  =  4.183,  the  mechanical  equivalent  for  converting  joules  to  calories, 
we  have 

,.  23070  v> 


This  is  simply  a  more  direct  method  of  deriving  Equation  (69)  . 

The  heat  AH  of  the  reaction  at  constant  pressure  and  at  temperature 
Tis: 

(108) 


The  quantity  J  is  accordingly  the  increase  in  heat  content  of  the  system 
at  the  absolute  zero  and  f  RT  the  value  of  AcPT  where  cp  is  the  specific 
heat  of  a  perfect  gas  at  constant  pressure. 

The  change  in  entropy  of  the  system  when  the  reaction  occurs  at 
constant  temperature,  obtained  directly  from  Equation  (105),  is: 

AS  =  |  RlnT  +  f  RlnMe  +  Si,  (109) 

in  which  we  have  neglected  the  slight  difference  between  the  molecular 
weights  of  the  ionized  and  the  neutral  atom. 

We  have  the  following    fundamental,  definitory  equation  of  ther- 
modynamics4 connecting  free  energy  with  heat  content  and  entropy: 

AF  =  AH  -  TAS.  (110) 

Introducing  the  values  of  AH  and  AS  from  Equations  (108)  and  (109) 
we  obtain 

AF  =  J  -  |  RTlnT  +  (f  R  -  %RlnMe  -  Si)  T.  (Ill) 

3  J.  Am.  Chem.  Soc.,  43,  pp.  1630-2  (1921). 

4  This  is  a  generally  accepted  definition  among  physical  chemists. 


THERMAL  EXCITATION  159 

The  equilibrium  constant  KP  by  definition  takes  the  following  form 
for  a  reaction  of  the  type  given  by  Equation  (106) 

..'•'/•:  Kr  =  ,,:  '  (112) 


where  p+,  p~,  and  p  denote  respectively  the  partial  pressures  in  the 
equilibrium  state  of  the  ions,  the  electrons  and  the  neutral  atoms. 

Now  for  any  reaction  there  is  a  perfectly  definite  relation  expressed 
by  Equation  (113),  between  the  change  in  free  energy  and  the  equilib- 
rium constant.  The  derivation  of  this  relation,  which  is  familiar  to 
chemists,  consists  simply  in  the  manipulation  of  thermodynamic  equa- 
tions, and  can  be  found  in  text  books  on  physical  chemistry. 

AF  =  -  RTlnKp.  (113) 

Substituting  the  value  of  AF  from  Equation  (111)  we  obtain: 

(114) 

On  changing  to  common  logarithms,  expressing  J  in  terms  of  Vi}  and 
substituting  the  other  numerical  magnitudes  mentioned  above,  we  find, 

7i+  .  n—  ^0^0  V 

log  Kp  =  log  E-j£-  =  -  25™LL<  +  2.5  log  T  -  6.69.         (115) 

This  is  the  reaction-isochore  by  which  we  may  compute  the  degree  of 
ionization  of  any  monatomic  vapor  as  a  function  of  the  temperature. 
If  x  represents  the  fractional  number  of  the  atoms  which  are  ionized, 
we  may  write 

T-' +  2.5  %  T7  -  6.69,  (116) 


rhere  P  is  the  total  pressure,  i.e.  P  —  p+  +  P"  +  P» 

SIMPLE  IONIZATION 

Sana5  has  employed  this  equation  to  compute  the  degree  of  ionization 
various  elements  at  high  temperatures.  As  a  particular  example  we 
give  in  Table  XXVI  his  computations  for  calcium  for  which  the  ioniza- 
tion potential  is  6.1  volts.  The  degree  of  ionization  is  expressed  in 
percentage,  pressure  in  atmospheres,  and  temperature  in  degrees  abso- 
lute. 

*  Proc.  Roy.  Soc.,  99,  pp.  135-53  (1921). 


160 


ORIGIN  OF  SPECTRA 


TABLE  XXVI 
THERMAL  IONIZATION  OF  CALCIUM  EXPRESSED  IN  PERCENTAGE 


Pressure 

j 

^~  —  -_^ 

10 

1 

10-1 

lO-2 

lO-3 

io-< 

io-« 

10~8 

Temperature 

2000° 

5-10-4 

1.4-10-3 

2500 

2-10-2 

7-10-2 

3000 

3-10-1 

1 

9 

4000 

2.8 

9 

26 

93 

5000 

2 

6 

20 

55 

90 

6000 

2 

8 

26 

64 

93 

99 

7000 

7 

23 

68 

91 

99 

7500 

11 

34 

75 

96 

• 

8000 

16 

46 

84 

98 

9000 

29 

70 

95 

10000 

46 

85 

98 

11000 

63 

93 

12000 

76 

96 

Complete  lonization 

13000 

84 

98 

14000 

90 

As  is  evident  from  Equation  (116),  the  percentage  ionization  increases 
with  (1)  increasing  temperature,  (2)  decreasing  pressure,  and  (3)  decreas- 
ing ionization  potential.  Calcium  has  a  medium  low  ionization  po- 
tential. It  is  therefore  interesting  to  contrast  the  figures  of  Table 
XXVI  with  those  of  Table  XXVII  for  atomic  hydrogen  which  has  an 
ionization  potential  of  13.5  volts.  At  the  temperatures  given,  the 
dissociation  H2  — >  2  H  can  be  readily  shown  to  be  complete,  so  that  we 
do  not  need  to  consider  the  molecule. 


THERMAL  EXCITATION 


161 


TABLE  XXVII 
THERMAL  IONIZATION  OF  HYDROGEN  EXPRESSED  IN  PERCENTAGE 


Pressure 
Temperature 

1 

10-1 

1C-2 

ID'3 

10-4 

io-5 

7000 

1 

4 

12 

8000 

2 

5 

18 

50 

9000 

2 

6 

20 

63 

90 

10000 

2 

6 

17 

49 

87 

99 

12000 

9 

28 

68 

94 

14000 

27 

65 

93 

16000 

55 

90 

18000 

80 

97 

20000 

92 

Complete  lonization 

22000 

97 

It  is  thus  seen  that  very  much  greater  temperatures  are  required 
to  produce  the  same  degree  of  thermal  ionization  in  hydrogen  than  in 
calcium  vapor  on  account  of  the  higher  ionization  potential  of  the  former. 
Caesium,  which  has  the  lowest  ionization  potential  of  all  the  elements  so 
far  measured,  should  be  completely  ionized  at  about  4000°  and  1Q-4 
atmospheres,  while  about  20,000°  at  the  same  pressure  should  be  neces- 
sary for  helium,  which  has  the  highest  known  ionization  potential. 


DOUBLE  IONIZATION 

The  analysis  for  the  simple  ionization  of  atoms  by  thermal  excitation 
lay  be  extended  so  that  the  fractional  number  of  atoms  which  are 
mbly  ionized  may  be  computed.  Using  calcium  as  an  example,  we 
ive  the  reactions: 


Ca  =  Ca+  +  E--  VJ/j     > 
Ca+  =  Ca++  +  E--  V?ffj\ 


(117) 


162  ORIGIN  OF  SPECTRA 

Here  F«*  corresponds  to  the  work  required  to  remove  the  second  electron 
from  the  atom  after  the  first  has  been  ejected.  As  discussed  in  the  latter 
part  of  Chapter  V,  this  is  determined  by  the  wave  number  1  @  for  metals 
of  Group  II  (cf.  Table  XX).  Its  value  is  54.2  volts  for  helium.  The 
spectroscopic  relations  are  unknown  for  metals  of  Group  I,  but  probably 
the  voltages  should  correspond  to  x-ray  limits  rather  than  to  highest 
convergence  frequencies  of  the  enhanced  spectra,  as  shown  in  column  7 
of  Table  XXII.  Nothing  is  known  of  the  values  of  Vt*  for  other  ele- 
ments. 

If  x  and  y  represent  the  fractional  number  of  Ca  atoms  which  are, 
respectively,  simply  and  doubly  ionized,  it  may  be  shown  that 

x  (x  +  2  y)  P  50507,    ,*ogy     „,      R    o 

**  =  —  6'59' 


If  we  confine  our  attention  to  the  temperature  and  pressure  ranges 
where  the  proportion  of  neutral  Ca  atoms  is  very  small,  we  may  put, 
approximately,  x  +  y  —  !•  Equation  (119),  which  then  alone  need  be 
considered,  takes  the  form: 


Since  V*  is  always  considerably  greater  than  Vt  it  will  necessarily 
require  a  much  higher  temperature  to  produce  the  same  degree  of  double 
ionization  as  of  simple  ionization.  For  example  with  helium  at  10"4 
atmospheres  but  77%  of  the  atoms  will  be  doubly  ionized  at  30,000° 
while  simple  ionization  is  practically  complete  at  20,000°.  Table 
XXVIII  gives  the  temperatures  at  which  several  elements  will  be  simply 
and  doubly  ionized  to  the  extent  of  50%.  By  means  of  the  above 
equations  one  will  readily  find  that  if  50%  of  the  atoms  are  just  simply 
ionized,  practically  none  will  be  doubly  ionized  (0.1%  and  less)  and  the 
remaining  50%  will  be  normal.  Similarly  if  50%  are  doubly  ionized, 
the  other  50%  will  be  simply  ionized  with  practically  no  neutral  atoms 
present.  The  temperatures  here  given  are  comparatively  high.  If 
lower  pressures  had  been  selected,  the  temperatures  would  have  been 
very  much  lower,  as  indicated  in  the  table  by  the  large  temperature 
change  from  a  pressure  of  1  to  0.01  atmosphere. 


THERMAL  EXCITATION 


163 


TABLE  XXVIII 
SIMPLE  AND  DOUBLE  THERMAL  IONIZATION 


Element 

50%  simply  ionized 
Practically  50%  normal 

50%  doublv  ionized 
Practically  50% 
simply  ionized 

98%  doubly  ionized 


Li..  .  . 

P  =  1 

P  =  0.01 

P  =  1 

P  =  0.01 

P  =  1 

P  =  0.01 

7800°  abs 
7500 
6600 
10300 
6300 
10100 
6000 
11000 
16000 
10200 
8600 
12000 
8100 
11600 
7500 
13000 

5300°  abs 
5100 
4400 
7100 
4300 
7000 
4100 
7800 
11500 
7100 
5900 
8400 
5500 
8100 
5200 
9200 

18000 
15000 
21000 
14000 
20000 
13000 
23000 

13000 
10700 
15300 
10000 
14700 
9200 
16500 

26500 
22000 
30500 
21000 
29500 
20500 
33000 

17000 
14000 
20000 
13500 
19000 
12500 
22000 

Na  ...... 
K  

Cu  
Rb  
Ae.  . 

Cs  
Au  
H  
Mg  
Ca  

Zn  

Sr  

Cd  
Ba 

Hg 

THERMAL  EXCITATION  WITHOUT  IONIZATION 

The  fact  that  we  have  been  able  to  derive  from  thermodynamic  con- 
siderations certain  quantitative  data  in  regard  to  thermal  ionization, 
which,  as  will  be  apparent  later,  seem  to  interpret  satisfactorily  phe- 
nomena heretofore  very  puzzling,  does  not  of  course  argue  that  heat  in 
itself  drives  an  electron  out  of  the  vapor  atom.  All  that  the  thermo- 
dynamic treatment  has  done  is  simply  to  give  a  statistical  survey  of 
the  actual  state  at  any  temperature  without  the  introduction  of  any 
postulates  as  to  how  the  ionization  is  produced  physically.  Since  at  any 
high  temperature  free  electrons  are  admittedly  present  in  the  vapor,  it  is 
likely  that  the  ionization  is  accomplished  in  part  by  collision  with  these 
electrons,  the  speed  of  which,  and  hence  the  number  capable  of  ionizing, 
increases  rapidly,  with  the  temperature.  Also  cumulative  ionization 
involving  absorption  of  radiation  must  play  an  important  role  at  high 
pressure,  as  discussed  in  Chapter  VI.  Howbeit,  it  is  of  interest  to  con- 


164  ORIGIN  OF  SPECTRA 

sider  in  the  above  statistical  manner  this  indirect  effect  of  tem- 
perature on  the  excitation  of  atoms  without  ionization.  For  example, 
let  No,'  represent  a  sodium  atom  in  which  the  valence  electron  is  in  the 
2  p  instead  of  the  normal  1  s  orbit.  For  a  mol  of  the  vapor  we  have  the 
reversible  reaction: 

Na  =  Na'  _  jn  (121) 

where  Jr  =  fVr/j,  the  quantity  Vr  being  the  resonance  potential  ex- 
pressed in  volts.  Since  both  the  normal  and  the  excited  atoms  are 
assumed  to  act  as  perfect  gases,  there  is  no  change  in  volume  or  pressure 
and  no  external  work  is  done.  Accordingly6  instead  of  Equations  (108) 
and  (109)  we  have: 

Atf  =  Jr,  (122) 

AS  =  0.  (123) 

Substituting  these  values  in  Equation  (110)  we  obtain: 

AF  =  Jr  (124) 

and  from  (113)  it  follows  that 

Jr  =  -  RTlnKp  =  -  RTln^  ,  (125) 

where  pf  and  p  denote  respectively  the  partial  pressures  of  the  excited 
and  normal  atoms.  If  we  confine  our  attention  to  such  a  temperature 
range  that  p'  is  small  compared  to  p  we  may  consider  p  to  be  approxi- 
mately the  total  pressure  and  p'/p  the  fractional  number  of  excited 
atoms,  whence, 

PL  =  e-w,  (126) 

p 
or 

N'  =  Ne-JSRT,  (127) 

where  N  is  the  total  number  of  atoms,  of  which  Nf  are  excited,  the 
latter  having  an  increase  in  energy  of  Jr  calories  per  mol  of  excited 
atoms.7 

As  an  example  we  shall  apply  Equation  (126)  to  sodium.     Since  Vr 
=  2.1  volts  we  find 

pf  24400 

•     —  =  e     T     for  sodium. 
p 

Table  XXIX  gives  the  fractional  number  of  atoms,  computed  from 
this  formula,  which  have  an  electron  in  the  2  p  orbit. 

e  This  method  of  derivation  was  suggested  by  Tolman. 

7  An  expression  equivalent  to  this  results  directly  from  probability  considerations.    See 
any  treatise  on  quantum  theory,  for  example,  Tolman,  Optical  Soc.  Am.  and  R".  S.  I.,  May 

(1922). 


THERMAL  EXCITATION  165 

TABLE  XXIX 

THERMAL  EXCITATION  OF  SODIUM 


Fractional  number  of 

Temperature 

atoms  with  electron 

in  2  p  orbit 

800  abs 

5-10-14 

1000 

2-10-11 

1500 

i-io-7 

2000 

5-10-6 

3000 

3-10-4 

A  similar  table  might  be  computed  for  an  orbit  of  greater  energy  level 
illustrated  by  Figure  5,  for  example  for  2  s  ,  or  3  d,  in  which  case  we 
should  find  a  higher  temperature  necessary  to  maintain  the  same  con- 
centration of  excited  atoms. 

FLAME  SPECTRA 

If  a  metal  is  vaporized  in  a  bunsen  flame,  an  emission  spectrum  is 
produced.  Usually  this  consists  of  the  first  pair  1  s  —  2  p  of  the  princi- 
pal series  for  the  alkalis  and  1  S  —  2  p2  and  sometimes  1  S  —  2  P  f or 
the  metals  of  Group  II.  Observations  on  the  alkalis  are  a  matter  of 
common  experience.  The  slightest  trace  of  sodium  vapor  in  the  bunsen 
gives  rise  to  the  D-lines.  Using  a  very  simple  device  of  McLennan 
and  Thomson8  in  which  a  small  furnace  surrounding  the  bunsen  main- 
tains the  heat  necessary  to  vaporize  the  metal  at  a  slow  and  constant 
rate,  the  flame  spectra  of  the  elements  of  Group  II  are  readily  observed, 
as  indicated  by  F  in  the  last  column  of  Table  XVI. 

In  general  we  may  conclude  that  the  fundamentally  important 
lines,  from  the  standpoint  of  atomic  theory,  are  those  which  appear  in 
the  low  temperature  flame.  These  same  lines  determine  the  values  of 
the  resonance  potentials,  as  discussed  in  Chapter  III.  They  appear  in 
the  arc  below  ionization,  as  shown  in  Figures  23  and  24.  They  are 
prominent  absorption  lines  of  the  normal  vapor  and  are  readily  reversed, 
as  shown  in  Figures  14  and  15.  They  are  the  "long"  lines  and  the 
"raies  ultimes"  as  discussed  in  the  latter  part  of  Chapter  V.  They  are 
the  result  of  the  ejection  of  an  electron  to  an  orbit  of  next  higher  energy 
level  than  the  normal  state  of  the  unexcited  atom. 


«  Proc.  Roy.  Soc.,  92,  pp.  584-90  (1916). 


166  ORIGIN  OF  SPECTRA 

These  lines  by  no  means  appear  in  the  flame  because  they  normally 
are  the  most  intense  lines  of  the  arc  spectrum  and  hence  by  contrast 
only  seem  to  be  excited  alone.  In  fact  usually  they  are  not  the  bright 
lines  of  the  arc  ;  especially  is  this  true  of  the  metals  of  Group  II.  Further- 
more one  may  photograph  a  low  temperature  sodium  flame  until  the 
plate  is  "  burned  up"  at  the  D-line  and  only  a  slight  trace  of  other  lines 
can  be  detected.  We  may  conclude  that  in  general  the  ratio  of  intensi- 
ties of  these  fundamental  lines  to  other  lines  is  extraordinarily  high  in 
the  flame.  We  have  in  the  bunsen  another  method  of  producing  single- 
line  or  two-line  spectra. 

When  a  salt  is  injected  in  the  flame  we  obtain  again  the  simple  single- 
line  spectrum  of  the  metal,  as  shown  in  Figure  28  A,  prepared  by  Meggers. 
Under  certain  conditions,  however,  other  lines  appear  faintly,  for  example 
lines  of  the  subordinate  series.  This  is  readily  explained  by  the  fact 
that  dissociation  of  the  salt,  such  as  NaCl,  by  the  flame,  gives  rise  to 
Na+  and  Cl~.  If  the  sodium  ion  captures  an  electron,  it  is  thereby 
able  to  emit  any  line  of  the  arc  spectrum.  Zahn9  estimates  that  each 
sodium  atom  in  a  bunsen  flame  fed  with  NaCl  emits  on  the  average 
2000  quanta  of  D-radiation  per  second.  It  is  readily  believable  with 
the  minute  partial  pressures  of  sodium  or  chlorine  in  a  flame  (order  of 
magnitude  10"6  mm  Hg  and  less)  that  the  probability  of  a  sodium  atom 
capturing  a  chlorine  atom  and  forming  NaCl  to  be  again  dissociated  is 
comparatively  small.  In  other  words  the  number  of  times  a  reaction 
of  the  form 


occurs,  which  may  involve  a  subsequent  reaction 

Na+  +  E-  =  Na, 

and  the  emission  of  all  arc  lines  is  small  compared  to  the  number  of 
times  the  reversible  reaction 

Na'-+Na 

takes  place  with  the  emission  of  the  D-lines.  Hence  while  the  dis- 
sociation of  NaCl  does  give  rise  to  all  arc  lines,  the  formation  of  Na', 
having  the  short  life  T  —  10~8  seconds  (page  93)  is  so  much  more 
frequent  that  the  intensity  of  these  fundamental  lines  is  extraordinarily 
high  relative  to  the  other  arc  lines.  The  main  service  of  the  salt  is 
accordingly  in  furnishing  a  carrier  for  the  metal  and  the  immediate 
spectroscopic  consequence  of  the  dissociation  is  incidental. 

•Verb.  Physik.  Ges.,  15,  pp.  1203-14  (1913). 


THERMAL  EXCITATION 


167 


Again  emphasizing  that  temperature  in  itself  may  not  be  the  cause 
of  the  excitation  of  a  neutral  atom  but  rather  is  the  source  of  some  other 
direct  cause,  such  as  high  electronic  velocities,  let  us  apply  the  foregoing 
statistical  reasoning  to  the  emission  of  light  from  a  bunsen. 

Zahn  observed  that  when  6.9-1013  sodium  atoms  per  sec.  were  fed 
into  a  bunsen  having  a  flame  propagation  of  510  cm/sec.,  a  rate  of  emis- 
sion of  D-radiation  resulted,  amounting  to  102  ergs/sec,  cm2,  as  shown 
by  photometric  measurements.  He  states  that  the  bright  flame  was 
3  cm  long  but  does  not  give  its  radius.  We  shall  assume  the  flame  to  be 
a  cylinder  1  cm  in  diameter.  Using  the  above  figure  for  the  rate  of 
emission,  we  accordingly  find  that  the  total  emission  of  the  flame  is  1014 
quanta/sec.,  which  is  Zahn's  experimental  value  expressed  in  other  units. 

The  volume  of  the  flame  is  2  cm3.    Hence 


number  of  Na  atoms /cm?  = 


6.9  -IP13 
2-510 


7  •  1010  at  any  instant. 


Let  us  consider  the  temperature10  of  the  flame  as  2000°  abs.     Referring 
to  Table  XXIX  we  find  that  the  fractional  number  of  atoms  in  the 
2  p  state  at  2000°  is  5-10~6. 
Whence 

No.  excited  atoms/ cm?  =  5  -  1Q-6  -  7  •  1010  =  3.5  -105 
and 

total  no.  excited  atoms  (2  cm?)  =  7  •  1C5  at  any  instant. 

The  average  duration  of  life  of  an  excited  atom,  as  discussed  in 
Chapters  IV  and  VI,  is  r  =  10~8  seconds.  Accordingly  the  number  of 
excited  atoms  formed  per  second  is  7-105  -f-  10~8  =  7-1013  =  1014.  This 
is  equivalent  to  the  number  which  pass  into  the  normal  state  each 
second  so  that  a  total  of  1014  quanta  per  second  of  D-radiation  are 
produced  within  the  flame.  Let  us  see  how  many  of  these  escape. 

At  atmospheric  pressure  the  number  of  atoms  per  cm3  is  2.7  -1019. 
Accordingly  the  partial  pressure  (p  mm)  of  the  sodium  atoms  is 

7-1010-760 
P  =     2.7- 10"     =  mm     g' 

Let  us  assume  that  at  any  instant  the  quanta  of  radiation  are  uni- 
formly distributed  throughout  the  cylindrical  volume.  The  quanta 
which  escape  will  be  those  which  pass  through  this  volume  to  the  outside 
boundaries  without  colliding  with  an  atom.  We  shall  assume  that  all 


recognize  the  academic  question  here  involved,  but  these  computations  are  suffi- 
itly  inexact  to  permit  the  assignment  of  "  temperature"  to  a  state  not  in  statistical  equilib- 


168  ORIGIN  OF  SPECTRA 

directions  of  propagation  of  the  quanta  are  equally  probable.  Pro- 
ceeding in  a  manner  somewhat  similar  to  that  discussed  in  Chapter  VI, 
Dr.  K.  T.  Compton  very  kindly  derived  the  following  expression  for  the 
authors,  giving  approximately  the  fractional  number  of  the  quanta 
which  escape. 

Fraction  = 


In  this  formula  X  is  the.  mean  free  path  of  a  quantum  at  the  pressure  p, 
as  defined  in  Chapter  VI,  a  is  the  radius  of  the  cylindrical  flame,  and 
h  its  height. 

In  the  discussion  following  Equation  (99)  we  show  that  the  mean 
free  path  of  a  quantum  is  p/p  where  p  is  an  absorption  constant  and  p 
is  the  pressure  in  mm  Hg.  Using  Wood's  value  of  p  determined  for 
mercury,  we  obtain  for  the  mean  free  path  X  =  (0.0007/p)  cm.  The 
value  of  p  is  probably  of  the  same  order  oi  magnitude  for  the  sodium  and 
mercury  resonance  lines.  Hence  with  the  present  data  we  have  X  = 
7-10~4  -T-  2-10~6  =  300  cm  for  the  mean  free  path  of  the  quantum  of 
D-radiation  in  this  particular  bunsen  flame.  The  values  of  h  and  a 
are  3  cm  and  0.5  cm  respectively.  Since  X  is  large  compared  to  h  or  a, 
the  above  formula  reduces  to 

Fractional  number  escaping  =  1  —  -  —  ^-  • 

A        O  A 

On  substituting  the  values  for  these  constants  we  find  that  299/300 
of  the  quanta  produced  in  the  flame  are  actually  emitted.  In  con- 
tradistinction to  arc  phenomena  discussed  in  the  chapter  on  cumulative 
ionization,  absorption  is  of  very  slight  importance  in  flame  spectra  on 
account  of  the  low  partial  pressure  of  the  metal  vapor.  Accordingly  we 
conclude  that  the  bunsen  flame  of  the  type  described  should  emit  1014 
quanta/sec.  The  observed  value  was  also  1014  quanta/sec,  in  complete 
agreement  with  theory. 

Zahn  has  also  made  observations  on  the  lithium  flame.  His  data 
show  that  under  specified  conditions  the  total  emission  of  the  flame 
amounted  to  1015  quanta/sec,  for  the  red  lithium  line.  The  value  com- 
puted theoretically  in  the  manner  illustrated  above  is  1016  quanta/sec.,  in 
satisfactory  agreeement  considering  the  assumptions  involved. 

If  the  temperature  of  a  flame  is  increased  by  the  addition  of  oxygen, 
other  lines  are  readily  excited.  Many  lines  of  the  principal  and  sub- 
ordinate series  of  sodium,  if  not  the  complete  arc  spectrum,  appear  in  the 


THERMAL  EXCITATION  169 

oxy-acetylene  burner  fed  with  sodium  or  its  salts,  and  the  same  phenome- 
non occurs  with  other  elements.  As  the  temperature  is  increased,  the 
valence  electrons  are  driven  to  successively  higher  energy  levels,  ulti- 
mately giving  rise  to  the  state  of  ionization.  We  may  therefore  correlate 
spectral  lines  with  temperature,  whether  or  not  this  be  the  direct  cause 
for  their  production. 

SPECTRAL  LINES  CORRELATED  WITH  TEMPERATURE 

If  a  metal  vapor  is  gradually  heated  in  a  furnace  we  observe  first  the 
emission  of  a  fundamental  line  of  the  type  1  s  —  2  p  or  1  S  —  2  p%. 
This  is  also  true  when  the  vapor  of  a  metallic  salt  is  heated.  We  have 
found  that  the  D-lines  produced  when  NaCl  is  raised  to  1000°  C  in 
vacuo  are  quite  brilliant.  Higher  stages  of  temperature  excitation 
progress  through  furnace  spectra,  which  have  been  investigated  by 
King11  from  2000°  to  3000°  abs,  spectra  in  the  carbon  arc  at  3900°, 
chromospheric  spectra  at  possibly  6000°,  photospheric  spectra  at  possi- 
bly 7000°,  spark  spectra,  to  stellar  spectra  at  temperatures  ranging  up 
to  30,000°.  Of  course  the  correlation  of  arc  and  spark  spectra  with 
temperature  is  complicated  by  the  superposed  electrical  excitation. 
As  discussed  in  Chapter  V,  spark  lines  may  be  excited  at  very  low 
temperatures,  with  a  proper  arrangement  for  producing  high  electronic 
velocities  by  electrical  means.  Hence  our  present  classification  must 
be  considered  as  very  qualitative. 

Accordingly  as  the  temperature  of  calcium  vapor,  for  example,  is 
increased,  we  should  first  have  no  emission,  but  rather  absorption  of 
fundamental  lines  belonging  to  the  series  IS  —  mp2  and  1  S  —  mP. 
On  further  increase  in  temperature  the  line  1  S  —  2  p2,  X  6573,  should 
appear  in  emission  and  when  the  temperature  is  sufficient  to  maintain 
a  fair  proportion  of  electrons  in  the  2  p2  orbit,  lines  of  the  subordinate 
series  should  show  absorption.  Gradually  the  line  1  S  —  2  P,  X  4227, 
puts  in  its  appearance  as  an  emission  line,  and  finally  all  arc  lines  are 
excited  when  the  thermal  ionization  becomes  pronounced.  If  the 
temperature  is  further  increased  until  a  fair  proportion  of  the  atoms 
are  simply  ionized,  the  arc  absorption  and  emission  spectra  fade,  and 
fundamental  lines  of  the  enhanced  spectra  such  as  1  ©  —  2  Si,2, 
X  3968  and  X  3933  appear  both  in  absorption  and  emission.  Later  other 
enhanced  lines  are  excited,  and  if  the  process  of  heating  is  continued  all 
the  atoms  will  be  doubly  ionized.  When  this  state  is  reached,  steps 

11  Long  series  of  papers  in  Astrophys.  J.  and  Mt.  Wilson  Contrib. 


170 


ORIGIN  OF  SPECTRA 


begin  toward  triple  ionization;  the  arc  lines  vanish  and  the  ordinary 
enhanced  lines  should  eventually  fade,  giving  place  to  enhanced  spectra 
of  the  ''second  type."  There  is  no  sharp  division  line  between  the 
various  spectra.  At  any  one  temperature  we  may  have  spark  lines 
from  ionized  atoms  and  arc  lines  from  neutral  atoms.  If,  however,  the 
temperature  is  great  enough  to  produce  much  double  ionization  it 
may  be  readily  shown  as  pointed  out  earlier,  that  most  of  the  atoms 
should  be  either  simply  or  doubly  ionized,  with  practically  none  in  the 
neutral  state.  Hence  if  we  have  present  the  enhanced  spectrum  of  the 
second  type,  all  arc  lines  are  absent.  In  other  words  but  two  types  of 
spectra  may  be  present  simultaneously.  Unfortunately  as  yet  we  have 
no  knowledge  of  the  higher  types  of  enhanced  lines,  so  that  this  deduc- 
tion from  theory  cannot  be  verified. 

If  we  select  a  fundamental  arc  line  such  as  1  S  —  2  P  and  a  funda- 
mental spark  line  such  as  1  @  —  2  ^  and  observe  the  ratio  of  intensity 
of  the  latter  to  the  former,  we  should  expect  this  ratio  to  increase  with 
the  temperature.  This  is  verified  qualitatively  by  King's  results  with 
furnace  spectra  and  other  data  from  the  spectroscopic  tables,  as  shown 
in  Table  XXX. 

TABLE  XXX 
RATIO  OF  INTENSITY  OF  1  @  —  2$  TO  IS  —  2 P 


Element 

Flame 

Furnace  °  Abs. 

Arc 
3900  "* 

Chromo- 
sphere 
6000 

Photo- 
sphere 
7000 

2000 

2300 

2600 

Ca 

0 
0 
0 

.06 
.03 
.1 

.05 
.05 
.1 

.06 
.06 
.09 

.8 
.7 
.8 

4 
20 
20 

40 

7 
4 

Sr  

Ba  

SOLAR  SPECTRA 

As  illustrated  by  Table  XXVI  the  degree  of  ionization  of  an  element 
depends  greatly  upon  the  pressure  as  well  as  the  temperature.  Thus 
the  pressure  differences  existing  in  the  sun  may  produce  a  wide  variation 
in  the  type  of  spectrum  excited.  Also  the  quantity  of  the  element 
present  is  of  importance.  Other  things  being  equal  we  should  expect 
lines  from  elements  present  in  relatively  large  amounts  to  be  the  more 
prominent.  If  the  element  does  not  exist  in  the  sun  its  spectrum  will 


THERMAL  EXCITATION  171 

be  absent.  However,  the  failure  to  detect  arc  lines  of  caesium  for 
example  is  insufficient  proof  that  the  element  is  not  present  even  in 
considerable  quantity. 

In  the  following  we  shall  review  some  of  the  recent  developments 
only  in  the  roughest  qualitative  manner.  For  more  detailed  informa- 
tion, all  necessarily  qualitative  however,  the  papers  of  Saha,1-2  Russell,13 
Milne14  and  others  should  be  consulted. 

The  solar  spectrum  should  be  characterized  by  lines  of  elements  in  a 
state  corresponding  to  that  at  about  6000  to  7000°,  and  4000°  for  a  sun- 
spot.  A  considerable  portion  of  the  alkalis  should  be  simply  ionized, 
especially  at  the  higher  levels,  where  the  pressure  is  less.  Although 
much  ionization  is  present,  enhanced  lines  should  not  appear,  for  as 
discussed  in  Chapter  V,  the  alkalis,  with  their  single  valence  electron 
removed,  are  not  in  a  condition  to  emit  or  absorb  enhanced  lines.  This 
requires  a  further  expenditure  of  energy  of  such  magnitude  that  at  least 
for  sodium,  potassium  and  lithium,  for  which  the  values  are  known, 
temperatures  of  7000°  are  insufficient.  One  may  fairly  definitely  state 
that  enhanced  lines  of  Na  and  K  are  absent  in  the  sun.  The  arc  spectra 
of  Li,  Na,  K  and  a  trace  of  Rb  are  present,  arising  in  the  small  percentage 
of  un-ionized  atoms  at  solar  temperatures.  The  failure  to  detect  Cs 
may  be  due  to  the  fact  that  the  element  is  absent  or  that  it  may  be 
nearly  completely  ionized  and  incapable  of  showing  arc  lines.  The  arc 
lines  of  the  alkalis  are  strengthened  in  the  sun-spots  on  account  of  the 
lower  temperature  and  resulting  lesser  degree  of  ionization. 

Table  XXVI  shows  at  6000°  a  considerable  proportion  of  ionized 
calcium  vapor  and  the  same  is  true  for  magnesium,  barium  and  stron- 
tium. We  find  in  the  solar  spectrum  both  arc  and  spark  lines  of  these 
elements  although  for  barium  many  of  the  arc  lines  are  absent  or  very 
faint.  The  arc  lines  of  Ca  and  Sr  are  strengthened  in  the  sun-spofcs. 
As  zinc  has  a  high  ionization  potential,  spark  lines  are  probably  absent, 
and  the  arc  lines  are  weaker  in  the  sun-spots. 

The  ionization  potential  of  helium  is  so  high  that  practically  no 
atoms  are  ionized.  Hence  we  may  now  understand  the  experimental 
fact  that  all  enhanced  lines  of  helium  are  absent. 

Hydrogen  also  is  not  ionized  except  possibly  at  the  very  highest 
levels  of  the  chromosphere,  and  then  scarcely  appreciably.  We  should 
expect  to  find  all  the  lines  of  the  Lyman  series  were  it  not  for  the  absorp- 
tion of  the  earth's  atmosphere.  A  small  proportion  of  the  atoms  have 

"  Phil.  Mag.,  40,  pp.  472-88  (1920);   40,  pp.  809-24  (1920). 
is  Astrophys.  J.,  55,  pp.  119-44  (1922);   55,  pp.  354-9  (1922). 
"  Observatory,  44,  pp.  261-9  (1921). 


172  ORIGIN  OF  SPECTRA 

electrons  in  the  second  orbit,  sufficient  to  account  for  the  reversal  of 
Balmer  lines  such  as  Ha. 

At  great  heights  above  the  reversing  layer,  where  the  temperature 
is  still  high  but  the  pressure  is  extremely  low,  simple  ionization  of  ele- 
ments having  a  fairly  low  ionization  potential  will  be  practically  com- 
plete, as  illustrated  by  Table  XXVI.  Accordingly  while  enhanced  lines 
may  be  emitted,  the  arc  spectrum  of  many  of  the  elements  should  be 
absent  in  the  high  level  chromosphere.  Mitchell  found  from  observa- 
tion of  the  flash  spectrum  that  the  H  and  K  enhanced  lines  of  Ca  ex- 
tended to  14,000  km  while  the  g  arc  line  terminated  at  5000  km.  The 
ionization  potential  of  Sr  is  lower  than  that  of  Ca  and  complete  ioniza- 
tion will  be  produced  at  higher  pressures  or  lower  levels.  The  flash 
spectrum  shows  that  the  arc  lines  of  Sr  disappear  before  those  of  Ca. 
At  pressures  below  10"3  atmosphere,  Na  is  completely  ionized;  in  the 
chromosphere  the  D-lines  reach  only  to  1200  km.  The  ionization 
potential  of  magnesium  is  the  highest  of  the  alkali  earths  and  the  arc 
lines  are  found  at  7000  km. 

Russell  points  out  that  the  behavior  of  Sc,  Ti,  V,  Fe,  Mn,  Cr,  Co 
and  Ni  in  the  spot  spectrum  is  intermediate  to  that  of  Ca  and  Zn  and 
states,  "It  may  be  surmised  that  the  ionization  potentials  for  these 
metals  lie  between  6  and  9  volts,  as  Saha  has  suggested  without  specify- 
ing his  reasons." 

STELLAR  SPECTRA 

The  temperatures  of  stars  are  usually  measured  by  observing  the 
spectral  distribution  of  their  radiant  energy,  just  as  has  been  done  with 
our  sun,  and  comparing  this  with  the  black-body  distribution  computed 
by  Planck's  law.  The  temperature  of  a  black  body  for  which  the  rela- 
tive spectral  distribution  most  nearly  fits  a  particular  stellar  distribution 
curve  is  considered  as  the  temperature  of  the  star.  Wilsing  and 
Scheiner15  and  others  have  made  such  observations  through  the  visible 
spectrum  for  a  large  number  of  stars,  and  Coblentz,16  using  a  spectroradio- 
metric  method,  has  been  able  to  extend  the  data  from  the  ultra-violet 
to  the  far  infra-red.  It  is  evident  from  what  has  been  discussed  in  the 
present  chapter  that  a  systematic  correlation  of  the  stellar  spectra  also 
permits  the  assignment  of  temperatures.  This  will  be  considered  more 
fully  in  the  following  paragraphs,  but  to  anticipate,  we  may  state  that 
such  computations  agree  fairly  well  with  the  temperatures  determined 

is  Wilsing,  Scheiner  and  Munch,  Pub.  Astrophys.  Obs.  Potsdam,  Vol.  24,  No.  74,  1920. 
"  Bur.  Standards  Sci.  Paper  No.  438. 


THERMAL  EXCITATION 


173 


from  the  black-body  distribution  without  reference  to  spectral  lines. 
This  is  illustrated  by  Table  XXXI,  in  which  the  data  of  Saha  were  ob- 
tained by  the  degree  of  ionization  method.  In  general  the  P  stars  are 
the  hottest  with  a  continuous  decrease  in  temperature  in  the  order  P, 
0,  B,  A,  F,  G,  K,  M,  N  to  R. 

TABLE  XXXI 
RANGE  OF  STELLAR  TEMPERATURES 


Stellar 
Class 

Typical  Star 

Wilsing  & 
Scheiner 
and  others 

Coblentz 

Saha 

Remarks 

Pb  

Great  Orion  Nebula 

15000 

_ 

__ 

PC  . 

I.  C.  4997  

30000 

Gaseous     nebulae 

Oa.... 

B.  D.  +35°,  4013.. 

23000 

23000 

with  bright  lines 

Ob  
Bo 

B.  D.  +35°,  4001.. 
c  Orionis  .... 

20000 

13000 

22000 
18000 

Hereafter,  all  lines 
are  dark 

B5  A 

q  Tauri.  .  . 

14000 

14000 

Ao  
ASF 

a  Canis  Majoris  .... 
ft  Trianguli  ... 

11000 
9000 

8000 

12000 

Fo 

a.  Carinae  

7500 

9000 

F5A... 
Go 

a  Canis  Minor  
a  Aurigae  

7200 
7100 

6000 
6000 

7000 

The  sun  is  a.  dwarf 

G5K 

a.  Reticuli 

4500 

star  of  this  class 

Ko 

a  Bootis 

3700 

4000 

K5M 

a  Tauri 

3500 

3500 

Ma 

a  Orionis  

3000 

3000 

5000 

Md.    .  . 

0  Ceti  

2950 

4000 

m 

W 

2300 

— 

, 

Table  XXXII,  taken  from  Sana's  paper,  is  a  compilation  of  the 
intensity  of  several  typical  lines  appearing  in  stellar  spectra.  Lines 
which  are  barely  visible  are  assigned  the  numeral  1.  The  symbol  0 


174 


ORIGIN  OF  SPECTRA 


HH       H 

—        - 

M    CQ 


n 

IS  1 


o 


O 


M 


^iSb 


|    | 


1  1  1  1 


b£  bC 


I    I 


THERMAL  EXCITATION  175 

denotes  a  line  the  intensity  of  which  cannot  be  obtained  from  the  Har- 
vard Annals.  An  interrogation  point  (?)  denotes  that  the  intensity  is 
not  stated  in  numbers  in  the  Harvard  Annals  but  is  compiled  from 
scattered  descriptions.  The  symbol  M+  denotes  that  the  line  is  due  to 
the  simply  ionized  atom  of  the  element  M.  This  table  shows  that  the 
lines  of  an  element  begin  to  appear  at  a  certain  stage,  rise  step  by  step 
to  a  maximum  and  disappear  at  the  other  end  of  the  scale.  Thus 
hydrogen  X  4860,  a  line  of  the  neutral  atom,  begins  to  appear  in  the 
low  temperature  Ma  stars,  reaches  a  maximum  in  the  hotter  A  group 
and  fades  out  as  the  temperature  increases,  finally  vanishing  at  Oc 
where  the  temperature  is  sufficient  to  ionize  hydrogen  completely. 
In  low  temperature  stars  the  arc  spectrum  of  calcium  is  prominent.  As 
we  progress  to  stars  of  higher  temperature,  spark  lines  appear,  arising  in 
ionized  atoms.  Further  increase  in  temperature  increases  the  propor- 
tion of  doubly  ionized  atoms  and  initiates  the  process  of  triple  ionization. 
The  arc  lines  vanish  because  neutral  atoms  are  no  longer  present.  Fi- 
nally the  spark  lines  fade  out,  giving  place  to  enhanced  lines  of  the 
second  type,  the  identification  of  which  is  yet  to  be  made.  A  similar 
development  may  be  carried  through  for  lines  of  other  elements. 

From  a  consideration  of  the  degree  of  ionization  of  the  elements,  a 

table  may  be  prepared  showing  the  characteristic  spectra  which  may  be 

expected  as  the  temperature  increases.     Saha  has  pointed  out  several 

striking  phenomena  in  this  manner,  which  are  briefly  summarized  in 

f  Table  XXXIII.     It  is  evident  from  this  table  that  a  star  which  shows 

j  lines  of  ionized  helium,  for  example,  must  have  a  very  high  temperature. 

The  new  field  which  Saha  has  opened  appears  to  offer  great  possibilities 

in  the  realm  of  astrophysics.    At  present  however  the  subject  is  in  only 

the  earliest  stage  of  development,  and  as  Russell  states,  it  will  require 

,   years  of  work  to  correlate  systematically  the  numerous  variables  involved. 


176 


ORIGIN  OF  SPECTRA 


TABLE  XXXIII 

IMPORTANT  STEPS  IN  THERMAL  IONIZATION 


Phenomena 

Stellar 
Class 

Tempera- 
ture 

Remarks 

Appearance  of  the  K  line  

Me 

4,000  K 

Beginning  of  the  ionization 
of  Ca 

Disappearance  of  the  g  line  

B8A 

13,000 

Ca  completely  ionized 

Appearance  of  Mg+  4481  

Go 

7,000 

Mg  considerably  ionized 

Disappearance  of  the  K  line  
Mg~*~  4481  disappears  

Oc 
Oa 

20,000 
23,000 

Ca+  completely  ionized 
Mg"*~  completely  ionized 

Appearance  of  4686 

B2  A 

17,000 

He  considerably  ionized 

Disappearance  of  4471  

Oa 

24,000 

He  completely  ionized 

(10-1  atm.) 

Appearance  of  Balmer  lines. 
Appearance  of  He  lines 

Mb 
Ao 

4,500 
12,000 

Appearance  of  the  2-quan- 
tum  orbits  of  H 

Appearance  of  2-quantum 

orbits  of  He 

Maximum  absorption  of  hydro- 
gen lines 

Ao 

12,000 

Maximum  concentration  of 
2-quantum  orbits  of  H 

Maximum  absorption  of  helium 
lines 

B2A 

17,000 

Maximum  concentration  of 
2-quantum  orbits  of  He 

Disappearance  of  4295  

B8A 

14,000 

Sr+  completely  ionized 

Disappearance  of  Balmer  hydro- 
gen lines 

Ob  • 

(10-1  atm.) 
22,000 

H  completely  ionized 

Disappearance  of  4686  

Pe 

25,000- 

He"*~  completely  ionized 

30,000 

176  A 


Joel  turn 


Strontium 

FIG  28A.  Bunsen  flame  spectra.  Swan  spectrum,  CO,  4314,  4737,  5165  A. 
vapor,  H2O,  3064  A.  Li,  6708;  Na,  5890,  5896;  Ca,  4227;  Sr,  4607  A. 
in  yellow  and  red  due  to  CaO  and  SrO. 


Water 
Bands 


A4800 

FIG.  29.     Emission  spectrum  of  iodine. 


Chapter  VIII 
Thermochemical  Relations 

ELECTRON  AFFINITY  OF  ATOMS 

We  have  mentioned  in  the  latter  part  of  Chapter  IV  that  excited 
atoms  may  possess  an  electron  affinity,  tending  to  pick  up  an  electron 
and  become  negative  ions.  This  is  also  true  of  many  diatomic  molecules 
in  the  normal  state,  and  on  page  76  we  showed  that  the  Bohr  hydrogen 
molecule  leads  to  a  value  of  1.6  volts  for  its  electron  affinity.  That  is, 
work  equivalent  to  1.6  volts  must  be  done  on  the  negative  molecular 
ion  to  reduce  it  to  the  normal  molecular  state. 

Certain  normal  atoms,  particularly  the  halogens;  are  known  to 
possess  an  attraction  for  electrons.  An  atom  of  a  halogen  gas  has  an 
outer  shell  containing  seven  electrons.  We  have  seen  that  there 
is  a  general  tendency  for  electrons  to  be  grouped  in  pairs  or  octets,  as 
such  a  grouping  represents  a  high  degree  of  stability.  The  halogen 
atom  tends  to  pick  up  an  extra  electron,  completing  its  outer  shell  of 
eight.  As  a  negative  ion  it  resembles  the  stable  rare  gases  in  structure. 
It  is  this  tendency,  for  example,  for  the  normal  chlorine  atom  to  complete 
its  outer  shell,  which  enables  it  to  attract  the  valence  electron  of  sodium 
and  form  the  compound  NaCl.  If  a  chlorine  atom  captures  an  electron 
and  thus  becomes  a  negative  ion,  work  must  be  done  on  the  ion  to  reduce 
it  to  the  neutral  condition.  This  work  may  be  expressed  in  volts  per 
atom  or  in  calories  per  gram  atom,  the  latter  referring  to  the  work 
which  must  be  done  to  reduce  1  gram  atom  of  the  gas  (i.e.  6.06  X  1023 
negative  atom-ions)  to  neutral  atoms. 

Franck1  in  a  very  suggestive  paper  has  recently  opened  a  new  field 
connecting  electron  affinity  with  spectroscopic  phenomena.  The 
system  neutral  halogen  atom  and  a  stationary  electron  just  outside  the 
atom  represents  the  initial  quantized  state  on  the  Bohr  conception.  The 
final  state  is  that  of  the  atom-ion  with  its  outer  shell  of  eight  electrons. 
If  the  electron  falls  directly  from  the  initial  state  of  energy  TF4  to  the 

'Z.  Physik,  5,  pp.  428-32  (1921). 

177 


178  ORIGIN  OF  SPECTRA 

final  state  of  energy  Wf  the  system  loses  an  amount  of  energy  Wt  —  Wf. 
This  is  assumed  to  be  radiated  as  a  single  quantum  of  wave  number  VQ 
so  that  Wt  —  Wf  =  IICVQ.  Since  Wt  —  Wf  represents  the  work  which 
must  be  done  upon  the  atom-ion  to  reduce  it  to  a  normal  atom,  the 
radiated  light  of  wave  number  VQ  is -a  direct  measure  of  the  electron 
affinity  E.  The  question  as  to  whether  intermediate  quantized  states 
may  exist  between  the  initial  and  final  configuration  may  be  of  little 
importance.  If  intermediate  states  do  exist  they  may  not  differ  materi- 
ally from  the  initial  state  since  the  field  in  the  neighborhood  of  a  neutral 
atom  must  decrease  with  a  high  power  of  the  distance.  Hence  we 
should  have  a  spectral  series,  the  first  line  of  which  is  nearly  as  short  a 
wave-length  as  its  convergence.  The  entire  series  should  lie  in  an 
extremely  narrow  spectral  region  which  for  the  present  may  be  con- 
sidered a  single  line. 

This  line  of  wave  number  v0  is  emitted  only  in  case  an  electron  of 
zero  velocity  is  captured.  However,  the  atom  may  attach  to  itself 
an  electron  which  initially  is  speeding  toward  it  with  a  velocity  v.  Possi- 
bly the  range  of  initial  velocities  may  not  be  large.  An  electron  of 
velocity  greater  than  that  corresponding  to  the  electron  affinity  might 
penetrate  the  atom  and  escape.  If,  however,  for  a  small  range  of  the 
velocity  v  the  atom  captures  the  electron,  the  energy  of  the  system  will 
be  altered  from  Wt  +  £  mv2,  initial,  to  "FT/,  final,  and  the  resulting  radia- 
tion will  be  given  by  the  equation : 

hcv  =  Wt  -  Wf  +  4-  mv*  =  hcr0  +  J  mv*.  (128) 

Since  the  term  ^  mv*  may  assume  any  value  equal  to  or  greater  than 
zero,  with  possibly  certain  restrictions  above  mentioned,  the  emitted 
radiation  is  a  continuous  spectrum  with  a  sharp  limit  on  the  long  wave- 
length side  corresponding  to  v  =  0,  and  with  gradually  decreasing 
intensity  toward  the  short  wave-length  side  representing  a  decreasing 
probability  of  the  capture  of  high  velocity  electrons  by  the  atoms. 

Figure  29  shows  a  spectrogram,  made  by  Steubing,2  of  the  emission 
spectrum  of  iodine.  We  find  a  region  of  bright  continuous  emission 
sharply  defined  on  the  long  wave-length  side  at  X  4800  ±  15.  Higher 
resolution  showed  that  this  was  perfectly  continuous  and  did  not  possess 
structure  characteristic  of  ordinary  band  spectra.  The  continuous 
radiation  was  shown  to  be  emitted  by  the  atom  rather  than  by  the 
molecule.  This  was  indicated  by  certain  tests  in  a  magnetic  field  and 
by  the  fact  that  it  increased  in  intensity  when  the  vapor  was  heated  to  a 

'  Ann.  Physik,  64,  pp.  673-92  (1921). 


THERMOCHEMICAL  RELATIONS 


179 


point  where,  at  the  pressure  employed,  the  greater  part  of  the  iodine 
must  have  been  dissociated. 

Using  for  VQ  the  wave  number  corresponding  to  the  observed  limit 
X  4800,  one  computes  for  the  electron  affinity  of  iodine  a  value  2.57  volts 
per  atom  or  59.2  kg.  cal.  per  gram  atom.  This  is  in  only  fair  agreement 
with  determinations  by  less  precise  means.  Unfortunately  in  this  new 
field  satisfactory  spectroscopic  data  are  not  as  yet  available  for  other 
elements. 

In  Table  XXXIV  is  a  summary  of  determinations  of  electron  affinity 
of  several  elements  by  the  spectroscopic  method  just  described  and  by 
two  other  methods  discussed  in  the  following  sections. 


TABLE  XXXIV 
ELECTRON  AFFINITY 


Method 

Spectroscopic 

Grating  Energy 

lonization 

Element 

volts  /atom 

kg.  cal.  /g  atom 

volts  /atom 

kg.cal./gatom 

volts  /atom 

kg.cal./gatom 

ci-. 

2.57 

59.2 

5.0 
3.8 
3.5 
2.0 

116 

87 
81 
45 

4.8 
3.1 

2.8 

110 
71 
64 

Br~ 

I-  

s--  

GRATING  ENERGY,  IONIZATION  POTENTIAL  AND  ELECTRON  AFFINITY 

On  the  assumption  that  in  addition  to  the  ordinary  Coulomb  force 
of  repulsion  or  attraction  between  the  charges  on  the  ions  forming  the 
crystal  structure  of  certain  salts,  there  exists  between  two  ions  a  repul- 
sive force,3  the  potential  of  which  is  inversely  proportional  to  the  nth 
power  of  the  distance  apart,  Born4  has  computed  the  grating  energy 
of  various  crystals.  This  is  the  amount  of  work  U  necessary  to  convert 
1  mol  of  the  crystal  into  free  positive  and  negative  ions,  and  its  com- 
putation is  purely  an  electrostatic  problem.  The  value  of  the  exponent 
n  depends  upon  the  form  of  the  lattice  space,  as  determined  by  x-ray 
analysis,  and  upon  other  physical  constants.  For  most  of  the  alkali 
halides  n  =  9.  To  discuss  the  assumptions  here  involved  or  to  enter 
into  a  consideration  of  the  details  of  the  problem  is  beyond  the  scope  of 


3  This  force  represents,  as  an  approximation,  the  electrostatic  fields  due  to  the  outer 
electrons  of  the  atoms. 

«  Verb.  Physik.  Ges.,  21,  pp.  13-24  (1919);   21,  pp.  679-85  (1919). 


180  ORIGIN  OF  SPECTRA 

this  book.  Suffice  to  say  that  determinations  of  grating  energies  have 
yielded  results  of  the  greatest  importance  in  many  fields  of  physics 
and  chemistry.  We  shall  indicate  here  in  the  most  elementary  manner 
how  spectroscopy  is  involved,  through  electron  affinity  and  ionization 
potential,  in  grating  energies. 

Let  us  consider  a  salt  of  the  form  RX  where  R  is  an  alkali  and  X  a 
halogen  atom.    All  heat  and  work  units  are  expressed  in  kg.  cal. 
Let 

[  ]      denote  solid  phase  or  crystalline  state. 
(  )      denote  gaseous  phase. 
D  =  heat  of  dissociation  of  |-  gram  mol  (1  gram  atom)  halogen  gas 

into  monatomic  gas. 
S  —  heat  of  sublimation  at  absolute  zero  of  1  gram  mol  metal  or 

salt. 
Q  =  heat  of  formation  of  the  salt  from  the  elements  in  the  ordinary 

state. 

J  =  Work  in  kg.  cal.  necessary  to  ionize  1  gram  mol  salt  or  metal. 
E  =  Electron  affinity  of  1  gram  atom  halogen  gas,  expressed  in 

kg.  cal. 
E~  =  1  gm.  mol  of  electron  gas. 


RX 
(RX)        U  JR 

l      i  •;.  •  i 

JRX—  (R)(Xr-  -Ex-  -(XMRHe) 

FIG.  30.     Dissociation  of  the  salt  RX. 

We  shall  consider  the  process  in  which  the  initial  state  contains 
ionized  vapor  atoms  or  the  metal  and  negatively  charged  vapor  atoms 
of  the  halogen  gas,  and  in  which  the  final  state  represents  the  solid 
crystal.  The  difference  in  total  energies  for  these  two  states  referred 
to  a  gram  mol  of  the  crystal  is  the  grating  energy  U  which  Born  com- 
putes from  purely  electrostatic  and  geometric  considerations  of  the  space 
grating.  Physically  the  transition  between  the  two  states  may  be 
made  according  to  the  two  schemes  shown  in  Figure  30.  We  shall 
start  with  (R)+  (X)~  and  go  to  the  right.  Traveling  against  the  arrow, 


THERMOCHEMICAL  RELATIONS  181 

work  must  be  done;  with  the  arrow,  the  reaction  gives  out  energy. 
The  first  step  requires  an  expenditure  of  the  work  EX)  resulting  in  a 
gram  atom  of  neutral  halogen  atoms,  positively  charged  metal  atoms 
and  electrons.  The  electrons  are  allowed  to  combine  with  the  ionized 
metal  atoms,  giving  up  the  energy  JR,  the  ionization  potential  in  heat 
units,  and  producing  a  gram  atom  of  monatomic  halogen  gas  and  a 
gram  atom  of  the  metal  gas.  In  the  next  step  we  allow  the  metal  gas 
to  condense,  giving  up  the  heat  of  sublimation  SR,  and  the  halogen 
atoms  to  combine  into  diatomic  molecules,  giving  up  the  energy  of  dis- 
sociation Dx.  The  product  is  1  mol  solid  metal  and  £  mol  molecular 
halogen  gas.  These  now  combine  into  the  solid  crystal,  giving  up  the 
heat  of  formation.  Of  course  the  reaction  need  not  proceed  in  exactly 
this  order.  The  step  involving  QRX  is  introduced  because  this  is  the 
quantity  the  chemist  measures  in  determining  heats  of  formation. 

Another  method  of  transition  between  the  initial  and  final  states 
is  shown  on  the  left  of  the  figure.  This  probably  more  nearly  represents 
the  true  physical  process.  The  positive  metal  ion  and  the  negative 
halogen  ion  react,  forming  the  gas  (RX)  and  give  up  the  heat  represented 
by  the  ionization  potential5  of  this  molecular  gas.  The  gas  is  then 
condensed  to  the  crystal  state,  during  which  process  it  gives  up  its  heat 
of  sublimation. 

From  the  above  considerations  we  may  write  at  once  the  following 
thermochemical  relations 

U  =  JRX  +  SRX  (129) 

and  U  =  -  Ex  +  JR  +  Dx  +  SR  +  QRX.  (130) 

Hence  knowing  the  grating  energy  U  and  the  heat  of  sublimation 
of  the  salt,  it  is  possible  to  compute  the  ionization  potential  of  the  salt 
from  Equation  (129).  Equation  (130)  gives  a  value  of  the  electron 
affinity,  which  as  discussed  above  determines  the  long  wave-length 
limit  of  the  continuous  spectrum  of  the  halogen.  Eliminating  U  from 
the  two  equations,  we  obtain  an  expression  for  the  ionization  potential 
of  the  salt  involving  important  physical  and  chemical  constants.  Un- 
fortunately for  the  salts  RX  neither  the  ionization  potentials  nor  the 
heats  of  sublimation  are  known.  It  is  doubtful  if  the  former  may  be 
determined  at  all  by  the  ordinary  methods  of  measurement.  The 
heated  vapor  appears  to  dissociate  very  readily  with  temperature  alone, 

6  Theoretically  other  types  of  ionization  may  exist  as  discussed  later.  In  the  example 
under  consideration,  however,  ionization  of  RX  in  the  vapor  state  without  doubt  produces 
dissociation  as  here  assumed.  For  the  present,  if  there  be  any  question,  we  may  consider 
this  to  be  a  definition  of  J^. 


182 


ORIGIN  OF  SPECTRA 


completely  masking  any  ionization  by  electronic  impact.  The  chemical 
data  involved  in  Equation  (130)  are  not  known  with  a  high  degree  of 
accuracy,  but  it  is  of  interest  to  compute  the  electron  affinity  of  several 
halogens,  using  what  meager  data  exist.  Equation  (130)  may  be  solved 
directly  for  Ex  and  the  experimentally  determined  values  substituted 
for  the  various  constants  or  we  may  obtain  the  same  result  by  consider- 
ing in  Table  XXXV  each  separate  step  in  the  reaction  illustrated  by 
Figure  30.  For  the  relation  between  volts/molecule  and  kg.  calories/ 
mol,  refer  to  Equation  (70).  We  shall  first  consider  the  salts  KC1, 
KBr  and  KI,  all  data  being  expressed  in  kg.  calories/mol  or  gram  atom. 


TABLE  XXXV 
ELECTRON  AFFINITY  OF  HALOGENS  FROM  GRATING  ENERGIES 


Reaction 

Cl 

Br 

I 

Remarks 

[KX]  =  (K)+  +  (X)~ 

-  163 

-  155 

-  144 

Bern's  grating  energies. 

[K]  +  *  (X2)  =  [KX] 

+  106 

+    99 

+    87 

Heat   of  formation:     cf.    Fajans, 
Verb.  d.  Phys.  Ges.,  21,  p.  716, 
1919. 

(X}  =  |  (X,) 
/          * 

+    53 

+    23 

+    18 

Heat  of  dissociation:    cf.  Fajans, 
idem. 

(K)  =  [K] 

+    21 

+    21 

+    21 

Heat  of  sublimation,  from  vapor 
pressure  curve. 

(K)+  +  E-  =  (K) 

+    99 

+    99 

+    99 

Ionization  potential,    Table    X, 

V    =    IS. 

m  +  E-  =  (xr 

+  116 

+    87 

+    81 

Electron    affinity,    kg.   cal./gram, 
atom. 

5.0 

3.8 

3.5 

Expressed  in  volts/atom. 

2440 

3350 

3490 

Expressed  in  Angstroms. 

Of  these  three  halogens  we  see  that  chlorine  possesses  the  highest 
electron  affinity.  A  similar  set  of  results  may  be  obtained  from  a 
consideration  of  other  alkali  halogen  compounds.  Equation  (130) 
may  be  employed  directly  in  the  following  manner,  using  chlorine  as  an 
example 


Q 


KCI 


-  163  +  99  +  53  +  21  +  106  =  116  kg.  cal./gram  atom. 


THERMOCHEMICAL  RELATIONS 


183 


It  is  noted  that  the  value  obtained  from  the  grating  energy  for  the 
electron  affinity  of  iodine  is  not  in  close  agreement  with  that  found  by 
Franck  by  the  direct  optical  method.  Part  of  this  discrepancy  may  be 
due  to  the  inaccurate  chemical  data  involved,  but  Born6  is  inclined  to 
attribute  it  to  the  computation  of  the  grating  energy.  Little  is  known 
of  the  existence  of  the  repulsive  force  between  the  atoms  in  the  crystal, 
and  it  is  likely  that  the  resulting  potential  energy  cannot  be  represented 
by  a  single  term  of  the  form  br~n,  an  additional  correction  term  being 
necessary. 

The  grating  theory  has  been  applied  to  other  types  of  compounds. 
For  example  Born  and  Bormann7  have  used  it  to  compute  the  electron 
affinity  of  the  sulphur  atom.  The  sulphur  atom  has  an  outer  shell 
containing  six  electrons.  In  order  to  form  the  stable  configuration  of 
eight,  it  possesses  a  tendency  to  attract  two  electrons .  It  may  therefore 
capture  the  two  valence  electrons  of  a  zinc  atom,  forming  the  compound 
ZnS.  The  zinc  atom  in  this  union  is  doubly  ionized,  while  the  sulphur 
ion  possesses  a  negative  charge  of  two  units.  Table  XXXVI  represents 
the  successive  stages  in  the  decomposition  of  this  compound. 

TABLE  XXXVI 
ELECTRON  AFFINITY  OF  SULPHUR  FROM  GRATING  ENERGY  OF  ZnS 


Reaction 

Heat 

Remarks 

[ZnS]  =  (Zn)-^  +OS)— 

-753 

Grating  energy  of  crystal,  computed  by  Born  and 
Bormann  and  later  corrected  by  Born. 

(Zn)    =[Zn] 

+   28 

Heat  of  sublimation  obtained  from  vapor  pressure 
data  and  other  data;  cf.  Born. 

iOSi)  =  [S\ 

+    14 

Heat  of  sublimation  to  diatomic  vapor  (Pollitzer)  . 

(S)      =  iGSi) 

+    52 

Heat  of  dissociation  (Budde). 

[Zn]  +  [S]  =  [ZnS] 

+    41 

Heat  of  formation  from  metallic  Zn  and  rhombic 
S  (Mixter). 

(Zn)++  +  2  E-  =  (Zn} 

+  663 

From  ionization  potential  Table  XI  and  work  re- 
quired to  remove  2d  electron,  Table  XX,  i.e. 

(1S  +  KS). 

(S}  +  2  E-  =  (S)~ 

+   45 
2.0 

kg.  cal./gram  atom  =  Eg  =  electron  affinity  for 
two  electrons, 
expressed  in  volts  /atom. 

•  Born  and  Gerlach,  Z.  Physik,  5,  pp.  433-41  (1921). 
»  Z.  Physik,  1,  pp.  250-55  (1920). 


184  ORIGIN  OF  SPECTRA 

The  electron  affinity  of  the  sulphur  atom  for  two  electrons  is  accord- 
ingly 2.0  volts/atom  or  45  kg.  cal./gram  atom,  a  value  which  will  be  used 
in  the  following  section. 


lONIZATION   OF   VAPORS   OF   COMPOUNDS 

Ths  simple  ionization  of  a  compound  molecule,  R^Xi,  may  result  in 
the  following  end  products: 

(a)  a  positive  molecular  ion  (RX)+  and  an  electron. 

(b)  a  positive  atom  ion  (R)+,  a  neutral  atom  X,  and  an  electron. 

(c)  a  positive  atom  ion  (R) +,  and  a  negative  atom  ion  (X)~. 

In  the  association  of  these  products  of  decomposition  and  the  formation 
of  the  original  molecule,  radiation  should  be  produced,  but  practically 
nothing  either  of  a  theoretical  or  experimental  nature  has  been  contrib- 
uted to  this  phase  of  spectroscopy.     A  material  ionizing  according  to 
(a)  may  possess  an  ordinary  series  line  spectrum,  an  example  of  which 
may  be  CO.     This  molecule  gives  a  definite  line  emission  spectrum,  but 
one  which  has  not  been  correlated  in  series.     Materials  ionizing  accord- 
ing to  (b)  or  (c) ,  besides  emitting  any  radiation  characteristic  of  associa- 
tion, should  show  the  line  spectrum  of  the  component  R.     The  former 
type  of  radiation  has  not  been  identified  as  yet,  but  the  latter  is  very 
commonly  observed.     For  example,  the  oxy-gas  flame  fed  with  NaCl 
shows  the  arc  lines  of  sodium.   The  molecule  is  dissociated  in  the  flame 
and  the  positively  charged  sodium  atom  picks  up  a  free  electron  instead 
of  the  negative  chlorine  atom.     Union  of  the  electron  and  sodium   ion 
gives  rise  to  the  arc  spectrum  of  sodium.     The  sodium  flame  emission 
is  known  to  be  suppressed  by  an  excess  of  chlorine.     This  is  due  to  the 
fact  that  with  a  large  number  of  chlorine  ions  present,  the  chance  of  a 
collision  between  the  positive  sodium  ion  and  the  negative  chlorine  ion 
is  increased  and  the  number  of  free  electrons  is  reduced  because  of  the 
electron  affinity  of  the  chlorine  atom  and  its  tendency  to  capture  a  free 
electron.     Hence  relatively  more  combinations  of  the  type  Na+  +  Cl~ 
take  place  than  of  the  type  Na+  +  E~,  with  the  resulting  decrease  in 
intensity  of  emission  of  sodium  lines.     Hydrogen  chloride  in  a  spark 
discharge  shows  the  spectrum  of  hydrogen  which  is  produced  in  the 
above  described  manner. 

The  ionization  of  a  molecule  of  the  type  RrXx  is  still  more  compli- 


THERMOCHEMICAL  RELATIONS  185 

cated  and  nothing  whatever  is  known  of  the  spectroscopic  relations. 
In  the  case  of  ZnCU,  for  example,  the  following  may  result  : 

(a)  (ZnClz)+  and  an  electron 

(b)  (ZnCl)+  and  (Cl)~  or  (Cl)  and  an  electron. 

(c)  (Zn)++  and  2  (Cl)~  etc. 

The  second  type  of  ionization  appears  very  likely  in  low  voltage  dis- 
charge. The  two  negative  chlorine  ions  are  probably  joined  to  opposite 
sides  of  the  doubly  charged  zinc  atom,  and  one  of  these  may  be  ejected 
by  a  single  electronic  impact.  Even  though  such  compounds  as  ZnCl 
are  incapable  of  stable  existence,  there  is  no  apparent  reason  why  they 
may  not  exist  momentarily  as  a  product  of  decomposition,  and  especially 
so  as  positive  ions.  In  fact  the  existence  of  ZnCl+  is  recognized  in 
electrolytic  dissociation. 

Lohmeyer8  has  studied  the  emission  spectra  of  the  mercury  halides 
HgCl  and  HgCl2.  Each  shows  a  characteristic  complicated  band  struc- 
ture, and  it  is  possible  that  these  will  be  interpreted  after  a  careful  con- 
sideration of  the  thermochemical  relations  involved. 

In  certain  cases  enough  chemical  data  are  known  to  enable  the 
prediction  of  the  ionization  potential  for  molecules  of  the  type  RX, 
assuming  they  are  ionized  by  dissociation.  As  an  example  we  shall 
consider  HC1,  HBr,  and  HI.  For  HC1  we  have 


+DH=  (H), 
+Dcl=  (CZ), 
(H)  +  JH  =  (H)+ 
(CQ  +  E-  -  Ecl  =  (CQ-, 


QHCI  +  DH  +  Dcl  +  JH-  Ecl  =  (#)+  +  (CO-         (131) 

The  last  five  terms  on  the  left  give  the  work  required  to  ionize  by 
dissociation  one  mol  of  hydrogen  chloride.  Hence  the  ionization 
potential  JHCi  of  HC1  vapor  may  be  computed  from  the  following 
equation 

JHCI  =  QHCI  +  DH  +  Dcl  +  JH-  Ecl.  (132) 

A  similar  relation  holds  for  HBr  and  HI.  Table  XXXVII  summarizes 
the  thermochemical  data  involved  and  shows  the  close  agreement 
between  the  computed  and  observed  ionization  potentials.  We  have 

«Z.  wiss.  Phot.,  4,  p.  367  (1906). 


186 


ORIGIN  OF  SPECTRA 


used  here  the  electron  affinities  determined  from  the  grating  energies, 
Table  XXXIV.  Hence  the  computed  values  may  be  in  error  by  several 
tenth  volts  from  this  source  alone.  The  value  13.7  volts  for  HC1  was 
obtained  by  the  authors  while  the  other  determinations  are  by  Knip- 
ping.9 

TABLE  XXXVII 

COMPUIED   AND   OBSERVED   lONIZATION   POTENTIALS   OF 

HC1,  HBr,  AND  HI 


HC1 

HBr 

HI 

Remarks 

QHX.. 

22 

12 

1 

From  Landolt-Bornstein. 

DH     

42^ 

42 

42 

Heat  of  dissociation  ^  gram  mol  Hj 

(Langmuir). 

Dx  

57 

23 

18 

Cl—  Pier;  Br—  Bodenstein  ;  I—  Starck  and 
Bodenstein. 

JH  

312 

312 

312 

Bohr  13.54  volts  —  confirmed  by  authors: 
cf.  Table  XV. 

-Ex  

-116 

-87 

-81 

From   Bora's   grating  theory;   cf.   Table 
XXXIV. 

JHX  

317 

302 

292 

Expressed  in  kg.  cal./mol. 

13.7 

13.1 

12.7 

Expressed  in  volts/molecule. 

i  13.7 
\  14.4 

13.8 

13.4 

Observed  values. 

It  is  evident  that  one  may  use  the  observed  values  of  the  ionization 
potentials  to  compute  the  electron  affinity  of  the  three  halogen  gases. 
We  accordingly  obtain  4.8,  3.1,  and  2.8  volts  for  Cl,  Br  and  I  atoms 
respectively.  The  value  for  iodine  is  closer  to  Franck's  determination 
by  the  optical  method  than  is  Born's  value  obtained  from  grating  energy. 
However,  this  may  be  accidental,  as  the  experimental  values  of  the 
ionization  potential  may  be  in  error  by  0.5  volt. 

Born  and  Bormann10  have  computed  the  ionization  potential  of 
hydrogen  sulphide  from  thermochemical  considerations  on  the  assump- 
tion that  the  molecule  is  dissociated  into  two  positive  hydrogen  atoms 
and  a  doubly  charged  negative  sulphur  ion.  While  computations  of 
this  kind  are  necessary  in  considering  energy  relations,  it  does  not  follow 

»  Z.  Physik,  7,  pp.  328-40  (1921). 
10  Z.  Physik,  1,  pp.  250-55  (1920). 


THERMOCHEMICAL  RELATIONS  187 

that  this  value  of  the  ionization  potential  would  be  observed  directly. 
In  a  low  voltage  arc  it  is  possible  that  only  one  of  the  hydrogen  atoms  is 
readily  ejected  by  a  single  impact.  This  would  permit  the  temporary 
existence  of  the  negative  ion  (HS)~.  If  such  an  ion  collided  with  another 
electron  the  second  hydrogen  atom  could  be  ejected,  producing  (S)  — 
and  (H)+.  The  computed  ionization  potential  31.8  volts  should  be 
accordingly  the  sum  of  these  two  observed  ionization  potentials.  The 
thermochemical  relations  for  complete  dissociation  are  as  follows: 

QM  =  (#2)  +  [SI, 


2(H)+2JH  =  2  (fl)+  +  2  E-, 
[S]  +  Ss  =  (S), 


QHtS  +  2  DH  +  2  JH  +  Ss  -  Es  =  2  (H)+  +  (S)—,     (132) 
/.  JB*  =  Qms  +  2DH  +  2JH  +  SS-ES  (133) 

=  5  +  84  +  624  +  66  -45 
=  734  kg.  cal./mol  =  31.8  volts/molecule. 

The  authors  have  observed  the  ionization  potential  of  ZnCU  as  12.9 
volts.  This  can  be  shown  from  a  consideration  of  the  thermochemical 
relations  to  be  far  less  than  the  value  necessary  for  complete  dissociation 
into  (Zn)++  +  2  (Cl)~.  Complete  ionization  of  this  compound,  as 
noted  earlier,  is  more  likely  a  two  stage  process  with  the  intermediary 
production  of  (ZnCl)~.  Table  XXXVIII  gives  a  summary  of  recent 
determinations  of  critical  potentials  in  compound  vapors. 

It  is  of  interest  that  with  zinc  ethyl  we  were  unable  to  obtain  the 
spectrum  of  zinc,  indicating  that  double  ionization  with  this  material 
in  our  apparatus  was  improbable. 

CKITICAL  POTENTIALS  AND  RADIATION  FKOM  ELEMENTS  IN  THE  POLY- 

ATOMIC STATE 

We  have  pointed  out  in  Chapter  III  that  the  quantum  relation 
hc2v  =  eV-  108  where  V  is  a  critical  potential,  cannot  be  safely  employed 
for  the  computation  of  characteristic  wave  numbers  for  elements  which 
are  polyatomic  in  the  vapor  state.  Of  course,  if  by  increasing  the 
temperature  of  the  vapor  a  sufficient  proportion  of  the  molecules  are 
dissociated  into  atoms,  the  critical  potentials  are  then  identified  with 
the  atom  and  the  quantum  relation  may  hold.  There  still  may  be 
exceptions  to  this,  however,  with  atoms  possessing  an  electron  affinity. 


188 


ORIGIN  OF  SPECTRA 


TABLE  XXXVIII 
RESONANCE  AND  IONIZATION  POTENTIALS  OF  MOLECULAR  COMPOUNDS 


Molecule 

Critical  I 

'otential 

Investigator  and  Remarks 

Resonance 

lonization 

HC1 

13.7 

Foote  and  Mohler. 

HBr     

14.4 
13.8 

Knipping. 
Knipping. 

HI 

13.4 

Knipping 

HCN    

, 

15.5 

Knipping. 

ZnCl2 

12.9 

Foote  and  Mohler 

CO  
H20  

? 
7.6? 

10.1 
14.3 

15.0 
13  ? 

Foote  and  Mohler  (two  ionization  po- 
tentials  and   inelastic   impacts   at 
6.4,  12.3,  14.0,  19.7,  22.3,  25.2,  27.7 
and  30.9  volts). 

Found  and  Stead,  and  Gossling. 
Foote  and  Mohler. 

HgCl2 

12.1 

Foote  and  Mohler. 

Zn(C2H5)2.. 
C4H10O  
C6H6  

7 
6.6 
6.0 

12 
13.6 

9.6 

Foote  and  Mohler. 
Boucher* 
Boucher. 

C7H8  
CsHio  
CHCI3. 

6.2 
6.5 
6.5 

8.5 
10.0 
11.5 

Boucher. 
Boucher. 
Boucher 

Phys.  Rev.,  19,  pp.  189-209  (1922). 


For  example,  we  have  found  a  pronounced  resonance  potential  in 
iodine  at  2.34  volts.  If  this  is  due  to  the  atom,  by  the  simple  quantum 
relation  we  should  expect  a  line  at  X  5300.  This  line  should  appear  in  a 


THERMOCHEMICAL  RELATIONS  189 

low  voltage  arc  and  should  show  absorption  when  a  long  column  of 
iodine  is  heated  to  a  point  where  a  considerable  amount  of  dissociation 
is  present.  Efforts  to  detect  this  line  as  well  as  the  corresponding  line 
for  arsenic  vapor  have  been  unsuccessful.  Of  course  there  are  thousands 
of  lines  present  in  this  region,  but  these  belong  to  the  complicated  mo- 
lecular band  spectrum  and  disappear  if  the  temperature  is  high  and 
pressure  low. 

Assuming,  in  the  critical  potential  measurements,  that  the  electronic 
impacts  occurred  with  dissociated  molecules,  it  is  quite  likely  that  the 
velocity  of  the  2.34  volt  electron  is  further  increased  on  account  of  the 
electron  affinity  of  the  iodine  atom.  The  total  kinetic  energy  absorbed 
should  then  be  not  2.3  volts  but  2.3  +  E.  This  might  give  rise  to  a 
resonance  line  at  2200  A  or  possibly  a  band  terminating  in  this  region. 
However  we  are  confronted  with  the  experimental  fact  that  an  electron 
of  higher  speed,  say  6  volts,  may  suffer  a  velocity  loss  of  2.3  volts  and 
leave  the  atom  with  a  velocity  of  3.7  volts.  What  becomes  of  the  energy 
corresponding  to  this  velocity  loss  of  2.3  volts? 

Various  facts  indicate  that  with  polyatomic  elements  the  ordinarily 
observed  critical  potentials  are  usually  characteristic  of  the  molecule 
rather  than  the  atom.  Accordingly  the  observed  resonance  potential 
might  represent  the  true  resonance  potential  of  the  atom  plus  the  work 
required  to  dissociate  the  molecule.  Similarly  the  ordinarily  observed 
ionization  potential  may  represent  the  true  ionization  potential  of  the 
atom  plus  the  work  of  dissociation  of  the  molecule.  Smyth  and  Comp- 
ton11  observed  two  ionization  potentials  in  iodine,  the  lower  one  being 
very  faint,  and  1.4  volts  less  than  the  more  pronounced  critical  velocity. 
The  work  required  to  dissociate  the  iodine  molecule  is  1.6  volts.  This 
lower  faint  ionization  appears  to  correspond  to  the  13.5  point  for  hydro- 
gen and  may  be  due  to  the  atoms  which  have  been  dissociated  by  the 
hot  cathode. 

Still  further  the  molecule  may  be  dissociated  by  the  impact  at  the 
observed  resonance  potential  and  the  impacting  electron  may  be  drawn 
into  one  of  the  atoms  on  account  of  the  electron  affinity.  The  char- 
acteristic radiation  should  then  be  located  in  another  part  of  the  spec- 
trum and  might  be  a  band,  a  line  or  a  group  of  lines.  If  we  consider  the 
electron  affinity  of  the  molecule  many  other  simple  possibilities  readily 
suggest  themselves. 

In  practically  all  cases  the  resonance  potentials  of  the  polyatomic 
elements  lead  to  wave-length  values  which  lie  in  a  region  of  strong  band 

»  Phys.  Rev.,  16,  pp.  501-13  (1920). 


190  ORIGIN  OF  SPECTRA 

absorption.  A  discussion  of  the  theory  of  band  spectra,  which  in  its 
present  initial  stage  of  development  is  summarized  by  Sommerfeld,12 
cannot  be  here  entered  upon.  The  theory  indicates  that  the  connection 
between  absorbed  energy  of  electronic  impact  and  final  radiation  as 
band  structure  may  be  involved  and  remote.  The  absorbed  energy  is 
distributed  between  the  quantized  vibratory  and  rotational  states  of 
the  molecule.  Brandt,13  using  the  photo-electric  method  of  measuring 
resonance  potentials,  found  for  nitrogen  some  twenty  inflections  in  the 
radiation  curve  (similar  to  Figure  25)  between  7.5  and  8  volts.  On  the 
Lenz  theory  these  might  correspond  to  the  same  final  but  different 
initial  momentary,  vibratory  and  rotational  quantized  states  of  the 
molecule. 

We  call  attention  to  the  above  facts  to  point  out  that  one  cannot 
use  the  method  of  critical  potentials  to  predict  new  series  in  polyatomic 
elements,  as  the  simple  relations  established  for  the  metallic  vapors  no 
longer  apply. 

If  the  resonance  potential  of  iodine  is  related  to  the  work  of  dissoci- 
ation, the  complicated  band  spectrum  may  appear  considerably  below 
ionization.  Experiments  indicate  that  the  reaction  2 1  — » I2  produces 
an  emission  of  these  bands.  Wood14  first  showed  that  iodine  vapor, 
heated  in  a  quartz  bulb,  emitted  the  complicated  band  spectrum.  The 
emission  is  better  demonstrated  by  using  a  large  graphite  heater  at  2000° 
C  in  the  center  of  a  glass  bulb  containing  iodine  at  rather  high  pressure. 
Strong  convection  currents  of  the  vapor  are  set  up.  The  molecules 
stream  from  the  bottom  up  the  center,  past  the  heater,  where  they  are 
dissociated,  and  then  flow  down  to  the  bottom,  following  the  walls  of 
the  bulb.  Above  the  heater  and  along  the  walls,  especially  in  the  upper 
part  of  the  bulb  where  recombination  is  taking  place,  the  yellowish-red 
illumination  in  the  vapor  is  brilliant.  There  is  no  emission  below  the 
heater  where  the  gas  is  in  the  diatomic  state,  nor  along  the  heater  where 
the  dissociation  is  occurring. 

It  is  certain  that  some  types  of  band  spectra  may  be  excited  by 
electronic  impact  at  a  voltage  less  than  the  ionization  potential.  Leon 
Bloch  and  E.  Bloch15  observed  the  positive  bands  of  nitrogen  at  12  volts 
and  the  negative  bands  at  21.5  volts.  They  accordingly  attribute  the 
positive  bands  to  the  neutral  molecule  and  the  negative  bands  to  the 
molecule  which  has  been  simply  ionized.  Meggers  and  the  authors16 

"  "  Atombau,"  3d  Ed.  (1922).    See  also  Birge,  Astrophys.  J.,  55,  pp.  273-90  (1922). 

"  Z.  Physik,  8,  pp.  32-44  (1921). 

14  "Physical  Optics,"  2d  Ed. 

«  Compt.  rend.,  173,  pp.  225-7  (1921). 

«  Unpublished  work  of  Jan.,  1921. 


THERMOCHEMICAL  RELATIONS  191 

investigated  the  emission  spectrum  of  nitrogen  in  the  presence  of  sodium 
vapor  which  was  introduced  in  order  that  the  ionization  of  the  latter 
might  increase  the  current.  A  discharge  tube  of  the  type  illustrated  by 
Figure  22  was  employed.  The  positive  band  group  of  nitrogen  appears 
at  7  volts  as  shown  in  Figure  31,  and  at  25  volts  the  negative  group  is 
intense.  The  range  from  18  to  25  volts  was  not  studied.  The  field 
recently  opened  in  the  experimental  study  of  band  spectra  from  the 
quantum  theory  standpoint  has  already  yielded  fruitful  results  and 
rapid  development  is  assured  within  the  next  few  years. 


Chapter  IX 
X-ray  Spectra 

INTRODUCTION 

The  radiation  phenomena  considered  in  Chapters  ill,  IV  and  V 
involve  primarily  the  valence  electrons  of  atoms.  The  corresponding 
phenomena  for  the  electrons  in  inner  atomic  orbits  will  be  considered 
in  the  present  chapter. 

X-ray  frequencies  are  in  general  higher  than  those  of  arc  and  spark 
spectra  since  the  electrons  are  closer  to  the  nucleus.  However,  the 
spectrum  range  extends  to  much  longer  wave-lengths  than  the  ordi- 
narily observed  x-ray  spectra,  and  overlaps  part  of  the  arc  and  spark 
range.  Measurements  with  the  crystal  grating  spectrometer  extend 
from  X  =  12  A  to  X  =  .1  A  or  in  terms  of  v/N  from  70  to  9000.  Meas- 
urements by  indirect  means  indicate  x-ray  wave-lengths  as  long  as 
700  A  or  v/N  =  1.3  and  no  definite  limit  in  this  direction  is  known  at 
present. 

A  fundamental  difference  between  x-ray  phenomena  and  valence 
electron  spectra  is  that  the  former  change  with  increasing  atomic  number 
from  element  to  element  in  a  continuously  progressive  manner.  This 
regular  sequence  is  evident  in  Figures  36  and  37,  showing  the  emission 
spectra  of  several  elements  on  the  same  scale.  The  approximate  law  of 
this  progression,  as  stated  by  Moseley,  is  that  the  square  roots  of  cor- 
responding frequencies  are  proportional  to  the  atomic  number.  The 
physical  basis  for  the  regularity  evidently  involves  a  similar  and  un- 
changing configuration  of  electrons  within  the  atom  combined  with  the 
increasing  nuclear  field.  We  have  derived  in  Chapter  I  a  fairly  accurate 
equation  for  Ka  on  the  basis  of  certain  assumptions  as  to  this  con- 
figuration. 

Besides  the  regular  change  in  frequency  of  x-rays,  there  is  also  a 
periodic  progression  in  the  complexity  of  spectra  as  successive  electron 
levels  are  added  to  the  atom  structure.  With  each  rare  gas  a  new 
electron  level  is  completed  and  another  x-ray  series  or  group  of  series 

192 


192  A 


• m 


192  B 


K  line  Klimit    R  limit  Br  L  lines  of  W 


r   i 


FIG.  32.     Photograph  by  de  Broglie,  showing  absorption  bands  of  silver  bromide 
superposed  on  the  emission  spectrum  of  tungsten. 


X-RAY  SPECTRA  193 

begins.  Table  III,  Chapter  I,  shows  the  order  in  which  these  levels 
appear  in  the  periodic  table.  In  the  first  row  we  have  one  inner  level 
determining  a  K  series;  with  neon  a  second  level  is  completed  and  the  L 
series  starts.  Similarly  we  assume  that  beyond  argon,  krypton,  xenon 
and  niton,  we  have  the  initiation  of  M,  N,  0  and  P  series. 

However,  our  knowledge  of  x-ray  spectra  is  not  as  extensive  as  the 
above  scheme  would  indicate.  Spectroscopic  data  cover  only  the  K 
series  from  sodium,  Z  =  11,  the  L  series  from  zinc,  Z  =  30,  and  the  M 
series  from  dysprosium,  Z  =  66.  This  range  has  been  considerably 
extended  by  experimental  methods  independent  of  spectroscopic  analysis 
as  well  as  by  combination  relations  of  spectral  lines,  but  0  and  P 
series  remain  largely  hypothetical. 

The  phenomena  of  x-ray  spectra  will  be  considered  under  the  sub- 
jects: (1)  Critical  potentials  for  x-ray  excitation,  (2)  Absorption  phenom- 
ena (including  the  transformations  of  absorbed  energy),  (3)  Emission 
lines  and  the  combination  principle  and  (4)  Theoretical  significance  of 
the  system  of  absorption  limits. 

1.   CRITICAL  POTENTIALS  FOR  X-RAY  EXCITATION 

An  important  difference  between  outer  and  inner  atomic  levels  is 
that  while  there  are  outside  of  the  atom  various  series  of  "  virtual  orbits" 
(positions  of  equilibrium  unoccupied  by  electrons  in  the  normal  atom), 
within  the  atom  all  positions  of  equilibrium  are  normally  filled.  Hence 
the  necessary  condition  for  excitation  of  x-rays  is  the  removal  of  an 
electron  from  the  atom.  Resonance  potentials,  single-line  emission 
spectra  and  line  absorption  spectra,  all  of  which  involve  removal  of  an 
electron  to  a  virtual  orbit,  are  absent  or  at  least  unobserved  in  high 
frequency  phenomena. 

Another  distinction  is  that  x-ray  frequencies  of  an  atom  are  in- 
dependent of  its  chemical  or  physical  state,  for  the  reason  that  the 
energy  levels  of  the  inner  structure  are  little  affected  by  the  outer  elec- 
trons which  are  alone  involved  in  chemical  reactions. 

The  above  statements  need  qualification.  There  is  no  sharp  dis- 
continuity between  the  principles  involved  in  outer  and  inner  atomic 
structure,  but  many  factors,  of  importance  near  the  surface,  become 
negligible  within  the  atom.  The  transition  stage  probably  lies  in  the 
little  known  region  between  the  ordinary  ultra-violet  and  x-ray  spectrum 
range. 

The  potential  required  to  excite  an  x-ray  series  can  be  accurately 


194  ORIGIN  OF  SPECTRA 

determined  with  the  Coolidge  tube.  D.  L.  Webster  and  his  associates1 
have  observed  critical  potentials  for  several  x-ray  series.  The  method 
involves  the  measurement  of  the  intensity  of  spectral  lines  at  potentials 
slightly  above  the  critical  point  and  the  extrapolation  of  the  intensity- 
voltage  curve  to  zero  intensity.  For  the  K  series  all  lines  start  at  one 
potential  and  above  this  point  maintain  their  intensity  ratios  constant. 
Critical  potentials  thus  measured  agree  within  the  experimental  error2 
with  limiting  frequencies  determined  spectroscopically. 

For  the  L  series  it  was  found  that  the  lines  occur  in  three  groups 
starting  at  potentials  corresponding  to  the  three  observed  limiting 
frequencies.  Four  critical  potentials  have  been  distinguished  in  the 
M  series  of  lead.  The  possibility  of  separately  exciting  the  different 
groups  of  the  L  and  M  series  is  of  fundamental  importance  in  the  inter- 
pretation of  emission  spectra. 

It  is  evident  that  with  sufficiently  sensitive  measurements  of  intensity 
it  might  be  possible  to  measure  critical  potentials  without  resolving  the 
radiation  into  a  spectrum.  X-ray  limits  should  then  appear  simply 
as  changes  in  slope  in  the  total  radiation-voltage  curve.  This  method 
has  been  most  useful  in  extending  x-ray  data  beyond  the  range  of  the 
crystal  grating.3  Since  all  materials  are  opaque  to  radiation  softer 
than  ordinary  x-rays,  the  radiation  is  detected  by  its  photo-electric  effect 
on  electrodes  within  the  x-ray  bulb.  In  this  manner  the  critical  po- 
tentials required  to  excite  the  softest  characteristic  x-rays  can  be  meas- 
ured. 

Table  XXXIX  summarizes  the  data  on  critical  potentials  obtained 
by  this  method.  The  results  of  the  authors  for  nickel  and  tungsten 
and  all  values  given  by  Kurth  and  other  observers  are  from  measure- 
ments of  the  radiation  of  solid  anticathodes.  The  other  potential 
measurements  of  the  authors  have  been  obtained  from  a  study  of  radi- 
ation from  a  thermionic  discharge  in  gas  (or  vapor)  at  low  pressure. 
The  radiation  intensity  from  a  gas  is  very  much  greater  than  from  a 
solid  target,  at  least  in  the  low  voltage  range.  It  is  essential  to  maintain 
conditions  such  that  electrons  receive  their  full  speed  before  collision 
with  the  gas  molecules  (see  description  of  experiments  on  low  voltage 
excitation  of  arc  and  spark  spectra;  Chapter  V,  Figure  22) .  The  photo- 
electric current  per  unit  cathode  current,  for  radiation  either  of  a  gas 
or  solid,  when  plotted  against  applied  voltage,  gives  a  nearly  straight 
line  with  change  in  slope  at  critical  potentials. 

i  Reference  1  at  end  of  chapter. 

«  See  Chapter  X. 

3  Reference  2  at  end  of  chapter. 


X-RAY  SPECTRA 

TABLE  XXXIX 

CRITICAL  POTENTIALS  AND  CORRESPONDING  FREQUENCIES  OP 
SOFT  X-RAYS 


195 


Element 

Z 

4 
5 

6 

7 
8 

11 
12 

13 

14  ! 
15 

16 
17 
19 
22 
26 

28 
29 

74 

Data  of 
Mohler  and  Foote 

Data  of  Kurth 

Series  limit 
given  by 
author 

Volts 

V/N 

Volts 

V/N 

Beryllium  .... 
Boron  

116 
186 

272 

374 

478 

35 
17 
46 
33 

126 
110 
95 
152 
122 
198 
157 
23 
19 

80 
.     60 

8.57 
13.7 
20.0 

27.6 
35.3 

2.58 
1.25 
3.40 
2.44 

9.30 
8.13 
7.01 
11.2 
9.02 
14.6 
11.6 
1.70 
1.40 

5.91 
4.42 

290 
33 

519 
50 

123 
150 

504 
145 
757 

227 
50 

1002 
297 
106 

21.4 
2.43 

38.3 
3.68 

9.11 
11.05 

37.2 
10.7 
55.9 
16.8 
3.69 

74.1 
21.9 

7.85 

K 
K 
K 
L 
K 
K 
L 
L 
L 
L 
L 
L 
L 
L 
L 
L 
L 
L 
L 
L 
M 
M 
L 
M 
L 
M 

if  0) 

M 

L 
M 

Ncn 

N 

Carbon 

Nitrogen  

Oxveien 

Sodium    ...    . 

Magnesium.  .  . 

Aluminum.  .  .  . 
Silicon  

Phosphorous.  . 
Sulphur 

Chlorine  

Potassium.  .  .  . 
Titanium 

Iron    

Nickel      

Copper 

Tungsten 

Data  of  Other  Observers 

Volts                v/N 

Richardson  and  Bazzoni             Carbon 
Molybdenum 
Hughes                                         Carbon 

Boron 

K  
M 

286                21.1 
356               26.3 
215                15.9 
34.5              2.55 
148                10.9 
24.5               1.81 

K  

L 

K 

L  

196  ORIGIN  OF  SPECTRA 

» 

Experiments  with  gases  show  that  ionization  takes  place  at  the 
critical  x-ray  potentials.  The  increase  in  ionization  is  not  as  pro- 
nounced as  the  radiation  change  and  in  only  two  elements  has  it  been 
studied,  sodium  and  potassium. 

It  is  seen  from  Table  XXXIX  that  measurements  of  critical  po- 
tentials cover  nearly  the  entire  interval  between  arc  spectra  and  the 
range  of  the  x-ray  spectrometer.  Most  of  the  work  has  been  concerned 
with  light  elements,  as  these  furnish  the  safest  starting  point  in  the 
development  of  new  methods. 

The  evidence  that  these  radiation  potentials  are  characteristic  x-ray 
limits  is  found  both  in  the  agreement  of  observed  potentials  with  limits 
computed  from  spectroscopic  data  (Figure  35),  and  in  the  Moseley 
relation  between  critical  potentials  and  atomic  number  (Figures  34  and 
35).  The  relation  of  these  data  to  x-ray  spectra  will  be  considered  in 
detail  later.  In  the  work  with  gases,  x-radiation  is  superposed  on  arc 
and  spark  spectra.  Many  fainter  potentials  not  listed  in  Table  XXXIX 
were  found,  but  it  will  require  further  study  to  classify  them. 

The  results  of  Hughes  are  apparently  inconsistent  with  those  of  other 
observers,  and  there  is  no  evident  explanation  of  the  difference. 

2.  ABSORPTION  PHENOMENA 

If  a  beam  of  continuous  (heterochromatic)  x-rays  is  passed  through 
a  thin  layer  of  any  element,  spectroscopic  analysis  of  the  transmitted 
light  shows  a  band  absorption  spectrum  characteristic  of  that  element. 
There  is  also  a  non-selective  absorption,  probably  caused  by  pure  scatter- 
ing of  radiation.  Only  the  selective  effect  will  be  considered  here. 
Figure  32  is  a  photograph  of  the  emission  of  a  tungsten  anticathode  in 
which  the  K  absorption  bands  of  the  elements  silver  and  bromine  in 
the  photographic  plate  are  distinctly  shown.  The  bands  are  regions 
of  continuous  absorption  terminating  abruptly  on  the  low  frequency 
side  and  fading  out  gradually  with  increasing  frequency.  The  position 
of  the  sharp  edge  of  each  band  coincides  with  a  limiting  frequency 
computed  from  critical  potential  measurements. 

Energy  absorbed  in  a  band  is  expended  in  the  ejection  of  an  electron 
from  the  atom.  Part  of  the  absorbed  energy  is  given  to  the  atom  and 
part  to  the  electron.  If  ~v\  is  the  frequency  of  incident  radiation  and  ~VQ  a 
limiting  frequency  characteristic  of  the  absorber,  then  an  absorbed 
quantum  of  energy  hv\  is  expended: 

(1)  In  work  on  the  atom,  hvQ] 

(2)  In  kinetic  energy  of  the  ejected  electron; 

i  mv*  =  hvi  -  hv0.  (134) 


X-RAY  SPECTRA  197 

This  is  identical  in  form  with  the  equation  originally  proposed  by  Ein- 
stein to  explain  photo-electric  phenomena  of  solids  in  the  visible  and 
ultra-violet  regions. 

One  consequence  of  Equation  (134)  is  that  each  absorption  limit  I 
determines  the  least  frequency  which  will  eject  an  electron  from  the  / 
given  level  of  the  atom.    Duane4  has  verified  this  very  accurately  for 
bromine  and  iodine.    A  beam  of  monochromatic  x-rays  was  passed 
through  an  ionization  chamber  containing  the  vapor  and  the  current 
measured  for  different  frequencies.     A  sharp  increase  in  the  ionization 
was  found  at  a  frequency  equal  to  the  K  limit. 

The  energy  hvo  given  to  the  atom  is  re-emitted  as  fluorescent  radi- 
ation when  the  ionized  atom  recombines.  It  was  known  even  before 
the  days  of  x-ray  spectroscopy  that  substances  exposed  to  x-rays  emitted 
a  characteristic  fluorescent  radiation.  As  the  excitation  of  an  atom  by 
radiation  is  identical,  in  its  effect,  with  excitation  by  electron  impact, 
viz.  complete  ejection  of  an  electron  from  one  of  the  inner  atom  levels, 
there  is  no  need  of  any  distinction  between  the  resulting  spectra. 

The  verification  of  Equation  (134)  requires  the  measurement  of 
velocities  of  photo-electrons,  ejected  by  radiation  of  a  frequency  greater 
than  the  absorption  limit.  The  method  of  measurement  developed  by 
Rutherford  and  recently  improved  by  M.  de  Broglie5  is  as  follows.  A 
thin  layer  of  the  material  studied  is  placed  in  a  narrow  groove  and  illu- 
minated by  x-rays.  A  magnetic  field  parallel  to  the  groove  bends  the 
photo-electrons  into  arcs  of  circles  of  radii  proportional  to  their  speed. 
This  dispersed  beam  of  electrons  falls  on  a  photographic  plate  giving  a 
"corpuscular  spectrum"  in  which  the  position  of  any  image  is  a  measure 
of  the  velocity  of  emission  of  a  group  of  photo-electrons.  If  an  element 
with  absorption  limits  K,  L  and  M  were  illuminated  by  x-rays  of  fre- 
quency v,  the  resulting  spectrum,  with  low  dispersion,  would  consist  of 
three  lines  corresponding  to  velocities  v\,  v2  and  ^3  given  by  the 
equations 

i  mv\  =  hv-K] 

i  mv\  =  hv  -  L  I  (134a) 

i  jYifi-i  =  hv  —  M 


In  practice,  intense  illumination  is  required  so  that  a  continuous 
x-ray  spectrum  is  used  rather  than  monochromatic  radiation.  The 
continuous  spectrum  of  maximum  frequency  v  then  gives  rise  to  a 


*  Reference  4  at  end  of  chapter. 
5  Reference  3  at  end  of  chapter. 


198 


ORIGIN  OF  SPECTRA 


"  corpuscular  spectrum"  consisting  of  bands  terminating  sharply  on  the 
side  of  maximum  velocity 

J  mv\  <  (hv  -  K)  (134b) 

etc. 
The  incident  x-rays  also  excite  characteristic  fluorescent  radiation  in 


15  30 

ATOMIC     NUMBER 


45 


60 


75 


90 


FIG.  33.  Moseley  diagram  of  absorption  limits  of  the  elements.  Dots  and  crosses 
are  limits  observed  spectroscppically  and  by  potential  measurements.  Circles 
are  values  computed  from  emission  spectra. 

the  material  illuminated  and  these  monochromatic  rays  give  rise  to  a 
corpuscular  line  spectrum  superposed  on  the  band  spectrum.  Thus 
lines  Ka,  K(3,  La.  and  Lp  of  the  fluorescent  radiation  produce  electrons 
of  velocities  corresponding  to  frequencies  Ka  —  L,  Kfi  —  L,  Ka  —  M, 
Kp  -M,La-  M,  L0  -  M . 


X-RAY  SPECTRA 


199 


De  Broglie  states  that  the  corpuscular  spectra  can  be  measured 
with  a  precision  comparable  to  spectroscopic  methods.  Evidently 
the  method  is  not  subject  to  the  limitations  of  the  crystal  grating  and  in 
the  future  it  may  prove  a  very  valuable  means  of  studying  atomic 
structure. 

As  absorption  limits  can  be  measured  with  a  precision  of  .1  %  or 
better  through  a  wide  spectrum  range,  they  furnish  our  best  means  of 
measuring  electron  energy  levels  within  the  atom.  De  Broglie  opened 
this  field  of  research.  The  precision  measurements  of  Duane  and  his 
associates,  together  with  the  work  of  Fricke,  Stenstrom,  Hertz,  and 
others,  furnish  a  basis  for  the  classification  and  interpretation  of  all 
x-ray  spectra.6 

The  K  series  absorption  limits  have  been  measured  for  nearly  all 
elements  from  magnesium  Z  =  12  to  uranium  Z  =  92.  As  critical 
potentials  have  been  measured  from  beryllium  Z  =  4  to  oxygen  Z  =  8, 
inclusive,  our  knowledge  of  the  innermost  energy  levels  of  the  elements 
is  nearly  complete.  The  K  limit  is  in  general  observed  as  a  single 
discontinuity  in  the  continuous  absorption.7  Figures  33  and  34  show 
the  K  limits,  for  the  light  elements,  plotted  on  the  Moseley  scale.  The 
points  all  fall  on  a  smooth  curve  which  is  nearly  linear  from  magnesium 
to  uranium.  Between  oxygen  and  magnesium  there  is  a  change  in  slope 
of  this  line.  The  ionization  potential  of  helium  at  25.5  volts  has  been 
included  on  these  diagrams.  It  falls  exactly  on  the  extrapolated  K 
line  and  is  evidently  the  starting  point  of  the  series. 

The  K  limit  of  uranium  is  of  peculiar  interest,  as  it  is  the  upper 
limit  of  the  range  of  atomic  line-spectra.  Duane's  measurements  give 
the  following  values  X  =  .1075  A;  •  v/N  =  8,476;  critical  potential 
114,770  volts.  Radiations  of  higher  frequency  than  this  exist.  Some 
of  the  hard  7  rays  may  be  of  very  much  shorter  wave-length,  but  these 
are  undoubtedly  vibrations  from  within  the  nucleus.  They  are  not 
strictly  speaking  characteristic  of  the  92  chemical  elements  but  of  the 
200  or  so  different  types  of  nuclei. 

L  absorption  limits  have  been  spectroscopically  measured  for  ele- 
ments Z  =  55  to  92.  Each  of  these  elements  shows  three  superposed 
bands,  of  which  the  long  wave-length  limit  is  strongest.  These  will  be 
designated  L  1,  L  2  and  L  3  in  order  of  decreasing  wave  length.8 

8  Reference  4  at  end  of  chapter. 

7  Absorption  limits  of  long  wave-length  in  this  and  other  series  show  a  fine  structure  at 
the  edge  of  the  band  which  will  be  discussed  later. 

8  The  notation  K  I,  L  1,  etc.,  serves  present  purposes  better  than  Kai,  Lai,  etc.,  used  in 
former  chapters.    It  avoids  confusion  with^he  line  notation  Km,  Lai,  etc.    Similarly  M  and 
N  limits  will  be  numbered  in  the  order  of  their  frequency,  the  lowest  being  1. 


200  ORIGIN  OF. SPECTRA 

L  limits  for  ten  light  elements  between  sodium  11  and  copper  29 
can  be  computed  from  critical  potential  measurements.  Here  too  the 
authors  have  observed  several  limits  for  each  element,  but  the  highest 
potential  corresponds  to  the  doublet  L  1,  2  and  the  other  limits  are  new 
series  not  found  in  heavy  elements.  Figure  35  gives  the  beginning  of 
the  L  series  and  Figure  33  the  entire  series.  The  ionization  potential 
of  Neon  at  16.7  volts  falls  on  the  line  L  1,  2  and  is  assumed  to  be  the  be- 
ginning of  the  series. 

M  series  limits  have  been  observed  spectroscopically  only  in  uranium, 
thorium  and  bismuth.  Five  limits  are  known  for  the  first  two  elements 
and  three  for  bismuth.  Four  critical  potentials  have  been  measured 
for  the  M  emission  lines  of  lead  and  Table  XXXIX  gives  potential 
measurements  of  M  limits  for  five  light  elements.  The  limits  ascribed 
by  Kurth  to  the  N  series  are  probably  M  limits.  Much  of  our  knowledge 
of  the  M  series  and  outer  levels  is  derived  indirectly  from  the  data  on 
emission  lines.  Detailed  consideration  of  the  relation  of  these  critical 
potentials  to  the  system  of  absorption  limits  will  be  given  later. 

In  the  above  treatment  of  absorption  phenomena  we  have  assumed 
that  the  limits  are  single  discontinuities  in  the  continuous  absorption. 
Stenstrom  and  Fricke9  have  obtained  spectrograms  with  relatively  high 
dispersion  which  indicate  that  this  is  not  the  case.  Fricke  describes  the 
structure  of  soft  K  limits  as  a  distinct  boundary  on  the  long  wave- 
length side  followed  by  an  absorption  line  or  band  and  sometimes  by 
two  bands.  The  interval  between  the  boundary  and  first  line  varies 
from  X  =  .002  A  to  .01  A  and  indicates  an  energy  difference  between  the 
levels  of  the  line  and  boundary  of  from  2  to  25  volts. 

Kossel10  has  suggested  that  this  line  absorption  may  be  ascribed  to 
the  virtual  orbits  outside  the  atom.  But  if  this  is  true,  the  boundary 
of  the  absorption  cannot  give  the  energy  required  to  remove  an  electron 
from  the  atom,  since  the  lines  are  of  higher  frequency  than  the  limit.  If 
the  lines  are  so  explained,  the  limit  of  the  band  may  give  the  work  re- 
quired to  displace  a  K  electron  to  the  incomplete  valence  ring.  Fricke 
states  that  the  structure  observed  is  apparently  not  consistent  with  the 
above  hypothesis.  Another  possible  theory  is  that  the  lines  are  limits 
for  multiply  ionized  atoms. 

The  potential  measurements  of  the  authors  gave  no  evidence  of  a 
structure  of  this  kind.  In  the  case  of  potassium  and  sodium  the  princi- 
pal radiation  potentials  agreed  within  experimental  error  (1  or  2  volts) 

9  Reference  4  at  end  of  chapter.  * 

10  Reference  5  at  end  of  chapter. 


X-RAY  SPECTRA 


201 


with  ionization  potentials  for  an  x-ray  level.    This  is  probably  the  most 
direct  evidence  that  x-ray  absorption  is  accompanied  by  ionization 


0  2466 

Atomic   Number 

FIG.  34.     K  limits  observed  by  the  authors  and  the  ionization  potential  of  helium. 

and  that  the  absorption  limit  corresponds  exactly  to  the  work  of  ioniza- 
tion from  an  x-ray  level.     Our  results,  however,  do  not  exclude  the 


202  ORIGIN  OF  SPECTRA 

possibility  of  excitation  without  ionization  at  other  critical  potentials. 
Some  faint  radiation  potentials  (not  listed  in  Table  XXXIX)  were 
observed  for  elements  of  the  first  row,  which  may  be  in  the  future 
identified  with  potentials  required  for  excitation  of  single  line  K  spectra. 
It  is  probable  that  in  the  outer  x-ray  levels,  the  phenomena  of  line 
absorption  and  resonance  spectra  become  of  importance.  With  valence 
electrons,  line  absorption  is  the  chief  characteristic,  and  continuous 
absorption  beyond  the  series  limit  very  faint,  while  with  high  frequency 
spectra  the  second  factor  becomes  predominant.  In  the  intermediate 
range  we  should  expect  to  find  the  transition,  although  conclusive 
experimental  evidence  of  this  is  yet  to  be  found. 

It  also  may  be  predicted  that  limits  of  x-rays  are  not  entirely  in- 
dependent of  the  chemical  and  physical  state  of  an  element.  Indications 
of  a  difference  in  K  limits  of  various  compounds  of  phosphorus  and 
chlorine  have  been  observed.11  On  the  other  hand  measured  K  limits 
of  four  carbon  compounds  showed  no  detectable  difference12  (less  than 
1  volt). 

The  possibility  of  locating  absorption  limits  by  measurements  of  the 
absorption  coefficient  of  elements  for  radiation  not  resolved  by  the 
spectroscope,  is  shown  by  Holweck.13  The  continuous  x-rays  from  a 
solid  bombarded  by  thermions  (electrons)  are  passed  through  screens 
of  very  thin  celluloid  and  the  absorption  coefficient  of  gases  and  solids 
for  the  residual  radiation  is  determined.  Now  the  continuous  radiation 
has  a  maximum  wave  number  v  given  by  the  applied  potential  V,  viz. 
v  =  8100  V.  If  this  radiation  is  passed  through  screens  exhibiting 
only  general  absorption  (no  bands)  in  the  region  studied,  the  lower 
frequency  radiation  will  be  entirely  absorbed  and  the  transmitted  frac- 
tion will  become  more  homogeneous,  approximating  monochromatic 
light  of  wave  number  v.  This  is  known  to  be  true  in  the  range  of  x-ray 
spectra  and  Holweck,  assuming  it  true  at  low  voltage,  was  able  to  esti- 
mate the  position  of  absorption  bands  from  curves  of  total  absorption 
vs.  potential.  Results  are  given  in  Table  XL,  together  with  comparison 
data  from  other  sources.  As  the  technique  of  the  measurements  is 
difficult,  the  agreement  must  be  considered  at  present  merely  as  a  satis- 
factory check  on  results  by  other  methods.  A  most  important  phase  of 
Holweck's  work  is  the  study  of  the  laws  of  non-selective  absorption  in 
the  low  voltage  range.  We  cannot  consider  this  subject  here  except  to 
state  that  the  results  justify  the  fundamental  assumptions  of  the  method. 

11  Reference  6  at  end  of  chapter.  12  Reference  2  at  end  of  chapter. 

13  Reference  7  at  end  of  chapter. 


X-RAY  SPECTRA 


203 


70  - 


10 


14. 


18. 


26. 


30 


ATOMIC    NUMBER 

IG.  35.     Soft  L  and  M  limits.     Dots  and  crosses  give  results  of  potential  measure- 
ments.   Circles  are  limits  computed  from  K  spectra. 


204 


ORIGIN  OF  SPECTRA 


TABLE  XL 
ABSORPTION  LIMITS  MEASURED  BY  HOLWECK 


X-ray  Limit 

Volts 

v/N 

Comparison  Data 

Carbon  K   

290  approx. 

21.4 

20.0      Mohler  and  Foote. 

Aluminum  L.  .  .  . 
Aluminum  K  
Boron  K      .... 

64  ±2 
1555  ±  10 
160  approx. 

4.7 
115.0 
11.8 

4.8      Figure  35. 
114.8      Fricke. 
13.7      Mohler  and  Foote. 

Gold  ATI,  2?  ... 

160  approx. 

11.8 

9         Figure  33. 

3.   EMISSION  LINES  AND  THE  COMBINATION  PRINCIPLE 

The  first  survey  of  the  field  of  x-ray  emission  spectra  was  made  by 
Moseley  soon  after  the  discovery  of  the  crystal  spectrometer  by  Bragg. 
Since  that  time  rapid  progress  has  been  made  in  the  precision  and  range 
of  measurements  and  particularly  in  the  discovery  of  new  lines  in  known 
series.14  Figures  36  and  37  show  typical  K  and  L  photographs.  Many 
more  lines  have  been  measured  than  can  be  seen  in  the  reproduction, 
and  the  complexity,  particularly  of  the  L  groups,  is  increasing  with 
every  improvement  in  technique.  Measurements  of  line  spectra  have 
been  extended  to  somewhat  longer  wave-lengths  than  absorption  limits. 

An  interesting  recent  development  is  the  extension  of  the  range  of 
the  diffraction  grating  by  Millikan.16  He  finds  isolated  groups  of  lines 
in  the  extreme  ultra-violet  spectra  of  sodium,  magnesium  and  aluminum 
which  he  ascribes  to  their  L  series.  The  wave-lengths  of  the  strongest 
of  these  are 

Na-372.2A,      Mg-232.2A,      A1-144.3A. 

The  above  lines  were  designated  as  I/a,  but  for  magnesium  and 
aluminum  the  wave-lengths  are  shorter  than  the  limit  LI.  A 
possible  explanation  of  their  origin  which  is  consistent  with  other  data 
will  be  given  later.  Similar  groups  of  lines  are  found  for  elements  in  the 
first  row  of  the  periodic  table.  These  are  apparently  related  to  the  L 
limits  of  carbon  and  oxygen  found  by  Kurth.  Though  the  theoretical 
significance  of  these  extreme  ultra-violet  emission  spectra  is  as  yet  in 
doubt,  they  at  least  promise  an  important  field  for  future  research. 

The  extensive  and  accurate  data  on  high  frequency  spectra  furnish 
us  the  basis  of  our  knowledge  of  the  inner  structure  of  the  atom.  An 


14  Reference  8  at  end  of  chapter. 


16  Reference  9  at  end  of  chapter. 


X-RAY  SPECTRA  205 

important  step  in  this  study  is  the  development  of  a  combination  princi- 
ple16 which  relates  emission  lines  and  absorption  limits  in  a  manner 
analogous  to  the  combinations  found  in  arc  or  spark  spectra.  A  system 
of  combinations  was  first  proposed  by  Kossel,  but  the  complexity  of 
absorption  limits  was  not  then  known,  and  the  scheme  is  too  simple  for 
a  satisfactory  interpretation  of  the  spectra.  In  the  past  year  several 
physicists  have  independently  developed  combination  principles  ade- 
quate for  the  explanation  of  nearly  all  observed  emission  lines. 

The  initial  condition  for  x-ray  emission  is  an  electron  deficiency  in  an 
inner  atomic  level.  The  emission  of  a  spectrum  line  results  when  an 
electron  from  an  outer,  orbit  falls  into  the  vacant  place.  The  final 
state  with  respect  to  this  process  is  accordingly  an  atom  with  an  electron 
deficiency  in  a  higher  level  and  the  process  is  then  repeated  until  the 
atom  assumes  the  normal  state.  The  quantum  radiated  is  equivalent 
to  the  difference  in  energy  of  the  two  successive  states  involved.  The 
energy  of  each  state,  referred  to  the  normal  as  zero,  is  proportional  to  a 
limiting  frequency.  Hence  the  frequency  radiated  should  be  equal  to 
the  difference  of  two  absorption  limits.  The  following  pages  give  the 
experimental  verification  of  this  conclusion. 

We  shall  consider  in  detail  the  x-ray  spectra  of  tungsten  consisting 
of  the  experimentally  determined  K  limit,  3  L  limits  and  over  30  emis- 
sion lines,  the  v/N  values  for  which  are  listed  in  Table  XLI.  These 
spectroscopic  data  with  a  few  exceptions  are  from  a  table  by  Smekal17 
and  data  of  Duane.18  The  notation  is  that  of  Siegbahn  as  revised 
by  Coster.17  The  system  of  combinations  follows  the  scheme  of 
Wentzel.17 

In  Figure  38  we  have  plotted  as  vertical  lines  the  differences 
between  absorption  limits  and  emission  lines.  Thus  in  the  lower  row 
are  plotted  K  1  —  Kai,  K  I  —  KaZ)  etc.  This  row  of  lines  gives  accord- 
ing to  the  combination  principle  the  energy  levels  involved  in  K  emission 
lines.  The  origin  is  the  atom  surface.  The  observed  ZJ  limits  plotted 
in  the  second  row  are  seen  to  agree  with  the  computed  values.  For 
convenience  L  and  M  series  are  plotted  on  a  larger  scale. 

In  the  computation  of  a  limit  from  an  L  line  we  must  first  determine 
which  of  the  three  L  limits  corresponds  to  the  initial  state.  Experi- 
ments by  Hoyt19  on  the  critical  potentials  of  tungsten  give  the  series 
limits  of  a  number  of  the  lines  (designated  by  *  in  Table  XLI)  and  the 
remaining  lines  are  classified  so  that  they  are  consistent  with  those  of 

16  Reference  10  at  end  of  chapter. 

17  Reference  10  at  end  of  chapter. 

18  Reference  4  at  end  of  chapter. 
i»  Reference  11  at  end  of  chapter. 


206  ORIGIN  OF  SPECTRA 

known  origin.  The  M  lines  are  assumed  to  originate  as  follows :  Ma  = 
M  1  -  N  1;  Mp  =  M  2  -  N  2;  My  =  M  3  -  N  3.  On  the  right  side 
of  Figure  38  are  shown  the  series  limits  of  the  emission  lines  which 
indicate  the  initial  states  involved.  The  plotted  differences  give  the 
final  state  for  each  emission  line  which  also  corresponds  to  an  absorption 
limit.  All  M  lines  are  plotted  on  one  row  and  the  M  limits  used  are 
those  computed  from  the  L  series  lines.  The  upper  row  gives  the  mean 
positions  of  five  M  and  seven  N  levels.  The  intervals  N  1,N  2  and  N  3, 


£ 

CO 


N  M 

234567  12               345 

t  II  III  II  .       I      I      I 

I  •-  M 

I       II  II  I  I  -L, 

III  I  I         -L, 

III.  II                                    I         — t-L, 

I  I          I  "K 


40                   80                 12O  ISO                2OO 

V/N  -L 

1  2    3 

|  |    |                       Observed 

I             II                                                  I  II                     — K 


200  400  600  80O  1OOO 

V/N 

FIG.  38.     Energy  levels  in  the  tungsten  atom  computed  by  the  combination  principle. 

NQ  for  tungsten  are  smaller  than  the  experimental  error,  but  for  uranium 
and  thorium  they  are  of  measurable  magnitude. 

In^Table  XLIps  given  the  origin  of  each  line  in  accordance  with 
Figure  38.  The  0  limits  are  all  unresolvable  and  close  to  the  origin,  so 
they  have  not  been  included  in  the  diagram.  All  but  two  very  faint 
lines  are  accounted  for.  It  is  seen  that  the  series  relationships  furnish 
a  logical  system  of  nomenclature  for  x-ray  lines  analogous  to  the  notation 
used  for  arc  and  spark  spectra. 


X-RAY  SPECTRA 


207 


TABLE  XLI 
X-RAY  SPECTRA  OF  TUNGSTEN 


Notation 

Observed 
r/JV 

Series  Notation 

Computed 
Limit  v/N 

Notation 

K  1 

51180 

Ka3  

4239 

Kl  -  L3 

879 

L3 

Ka2  

4270.3 

K  1  -  L2 

848 

L2 

Ka  1 

4368  7 

K  I  —  L  1 

749 

LI 

K/3.. 

4947.4 

K  1  -  M3 

171 

M  3 

KB'  . 

4928 

Kl  -  M  4 

190 

M  4 

Ky  

5050.9 

K  I  -  N  5 

27 

JV5 

LI 

75088 

L2  

849.42 

L3  

889.9 

LI 

544  02* 

LI  -  M5 

206  9 

M5 

La  2  

613.85* 

LI-  M2 

137.0 

M2 

Lai.        .    . 

618  45* 

L  1  —  M  1 

1324 

Ml 

L?/...... 

642.78* 

L2  -  M  5 

207.0 

M5 

L£4.. 

701  66* 

£3  _  jif  4 

1882 

Af  4 

L6Q  . 

708  00* 

LI  —  N  7 

429 

N  7 

L81.. 

712.39* 

L2  -  M2 

137.4 

M2 

L/33.. 

723  23* 

L3  —  M3 

166  7 

M3 

L/32  

733.76* 

LI-  AT4 

17  1 

N4 

L/3  8  

7364 

L37. 

746  6* 

L  1  -  N2 

43 

N2 

L/3  5  

751.1* 

L  1  -  0 

0 

0 

7520 

753  3 

jr.  Q       /if  2 

136  6 

M  2 



757.1 

L3  -  Ml 

132  8 

Ml 

Ly  5  

807.03 

L2  -  JV7 

42.7 

N7 

Ly  1  

831.81* 

L2  —  AT4 

17.9 

N4: 

844.2 

L2  -  N2 

5  5 

N2 

I/T6. 

8505 

L2  -  0 

o 

0 

Ly  2.  .  . 

854.98 

L3  -  AT6 

34.9 

NQ 

L-yS.  . 

859.97 

L3  -  AT5 

300 

AT5 

873  5 

L3  —  N  3 

16  4 

N  3 

Z/y4.  . 

887.77* 

L3  -  Nl 

2.1 

ATI 

Ma. 

13056 

M  1  —  ATI 

20 

Nl 

M0  

134.99 

M  2  -  AT2 

20 

N2 

MT.. 

149.62 

M3  -  N3 

17  1 

N3 

*  Denotes  lines  of  experimentally  determined  series. 


208  ORIGIN  OF  SPECTRA 

Figure  39  shows  the  M  and  N  levels  of  uranium  computed  from 
the  L  and  M  series.  In  this  case  the  five  M  levels  have  been  observed 
spectroscopically  so  that  the  N  limits  computed  from  M  lines  are  much 
more  accurate  than  for  tungsten.  Other  heavy  elements  give  similar 
results  and  for  atoms  as  light  as  caesium,  Z  =  55,  several  M  and  N 
levels  may  be  located  from  data  on  the  L  series.  L  limits  may  be  com- 
puted from  K  series  lines  down  to  magnesium,  Z  =  12.  K  spectra  for 
elements  lighter  than  titanium,  Z  =  22,  become  complicated  by  addi- 
tional lines  Kaf,  Kaz,  Ken,  Kab,  Ka&,  and  L  limits  computed  from  these 
lines  are  all  softer  than  L  1,  2.  Figure  35  shows  lines  drawn  through 


N 

1                         1                         I                         1 

M 

12   34  567 
II      II    II 

123              45 

1!      1         II. 

II   1       -if 

*>  M 

(I)              ||            Observed 

III 

:;|        i     i      i    •::•;:—  u 

II  II       1 

I 

II                        1          —  L, 

i                  i                  i                  i 

10O  200  500  40O  50O 

V/N 

FIG.  39.     Energy  levels  in  the  uranium  atom  computed  from  L  and  M  spectra. 

the  mean  points  computed  from  the  close  doublets  a3,  a4  and  ab)  a6.  It  is 
seen  that  the  computed  points  agree  with  the  observed  critical  potentials, 
though  only  in  one  case,  phosphorus,  were  the  three  potentials,  cor- 
responding to  the  three  lines  drawn,  clearly  separated. 

Several  theories  have  been  proposed  to  explain  these  a  lines  all  of 
which  assume  that  the  simple  combination  law  cannot  be  applied;  i.e. 
that  the  limit  K  1  does  not  determine  the  initial  state.  The  observation 
of  L  limits  agreeing  with  the  computed  frequencies, 

L  5,  6  =  K  1  -  Ka^  etc., 


208  A 


• 

4 

'JJ 

•' 

. 

* 

,»' 

J 

J 

,3 

• 

_,_ 

j     , 

1 

'»• 

>     0,J 

.45 

• 

Se 

} 

' 

Br 

Rb 

" 

_J 

Sr 

Nb 

Rh 

FIG.  36.     K  emission  lines  photographed  by  Siegbahn.     (Reproduction  is  a  negative.) 
The  line  at  the  left  is  a  reference  line.     The  strongest  close  doublet  is  K  ai  and 


208  B 


Tl 


Pb 


Di 


FIG.  37.      L  Spectra  photographed  by  Siegbahn.     Lines  from  right  to  left  are: 
a  group,  j8  group,  7  group  and  reference  line. 


X-RAY  SPECTRA  209 

cannot  be  explained  by  any  such  theory.  For  the  same  reason  we  can- 
not ascribe  these  L  limits  to  resonance  potentials.  If  the  K  limit  is  an 
ionization  potential,  L5,6  must  be  one  also,  provided  the  above  relation 
has  a  physical  basis. 

4.   THEORETICAL  SIGNIFICANCE  OF  THE  SYSTEM  OF  ABSORPTION  LIMITS 

It  is  evident  from  Figure  33  that  the  usual  assumption  that  the 
atom  structure  is  made  up  of  single  K,  L,  M,  etc.,  levels  is  a  very  rough 
approximation.  In  a  heavy  element  the  five  M  limits  and  seven  N 
limits  each  cover  a  range  of  frequency  comparable  to  the  interval  sepa- 
rating the  two  groups.  For  uranium  we  must  have,  in  addition  to  the 
sixteen  limits  shown,  an  undetermined  number  of  0  and  P  levels. 

Disregarding  for  the  instant  the  complexity  of  the  limits,  we  see 
that  the  magnitude  of  the  frequencies  involved  indicates  the  total 
quantum  number  n,  which  must  be  assigned  to  each  group  of  levels 
K,  L,  M,  etc.  Thus  the  energy  of  a  X-level  is  a  little  less  than  that  of  a 
single  electron  in  an  n  =  1  orbit  around  a  nucleus  of  charge  Ze.  An 
electron  in  an  outer  level  has  energy  comparable  to  an  electron  in  a 
higher  quantum  orbit  revolving  around  a  charge  (Z  —  z)e,  (z  =  electron 
deficiency)  so  that  to  a  first  approximation  the  equation  of  a  limiting 
frequency  is 

V/N  =  (Z~*)2-  (135) 

While  this  equation  is  far  from  accurate,  yet  it  indicates  that  n  has  the 
values  1  for  K,  2  for  L,  3  for  M ,  and  4  for  N. 

There  are  some  striking  regularities  in  the  complicated  groups  of 
absorbtion  limits.20  They  may  be  classified  in  two  ways:  (1)  Pairs 
LlL2,MZM4,MlM2,N5N6,N3N4,SMdNlN<2,  which  are 
converging  lines  on  the  Moseley  diagram.  The  wave-length  difference 
for  each  pair  is  constant  for  different  elements.  (2)  The  pairs  L  2  L  3, 
M  4  M  5,  M  2M  3,  N  6  N  7,  N  4  N  5,  N2N3  give  parallel  curves  on 
Figure  33.  The  law  of  their  separation  is  then  \/vi  —  \/7t  =  constant. 

It  was  shown  in  Chapter  I  that  the  separation  L  1,  2  could  be  ex- 
plained by  the  difference  in  relativity  correction  for  two  orbits,  one  of 
radial  quantum  nr  =  0  and  azimuth  quantum  na  =  2,  the  other  nr  =  1 
and  na  =  1.  Sommerfeld  finds  that  all  doublets  of  the  first  type,  AX  = 
constant,  can  be  explained  in  the  same  manner. 

20  Reference  1 1  at  end  of  chapter. 


210 


ORIGIN  OF  SPECTRA 


The  equation  for  this  doublet  separation,  Equation  (62)  Chapter  I, 
can  be  written  in  the  form 


7  (Z  -  z)4[l  +  a  (Z  -  z)2  +  b  (Z  -  z)4]  (136) 

where  7,  a  and  b  are  constants  involving  the  values  of  na  and  nr  used, 
and  z  is  the  electron  deficiency  in  the  orbit  concerned.  Values  of  na  and 
nr  are  chosen  according  to  the  scheme  of  Table  XLII. 

TABLE  XLII 
QUANTUM  NUMBERS  OF  X-RAY  LIMITS 


Limit 

K 

LI 

L2 

L3 

Ml 

M2 

M3 

M4 

M5 

ATI 

A'2 

AT3 

AT4 

AT5 

#6 

#7 

tin  . 

1 

0 
1 

2 
0 
2 

1 
1 
2 

1 
1 
2 

3 
0 
3 

2 
1 
3 

2 
1 
3 

1 
2 
3 

1 
2 
3 

4 
0 

4 

3 
1 
4 

3 
1 
4 

2 
2 

4 

2 
2 

4 

1 
3 
4 

1 
3 

4 

nr 

na  +  nr. 

That  the  law  AX  =  constant  is  consistent  with  Equation  (136)  is 
easily  seen.  To  an  approximation,  from  Equation  (135),  it  follows 
that  for  a  given  line  of  a  given  series  in  all  elements, 

v  =  k  (Z  -  z)2  z/2  =  fc2  (Z  -  z)4. 

By  Equation  (136),     Av  =  k'  (Z  -  z)4. 

Since  AX  =  Av/v2  we  have  AX  =  k'/k2  =  constant. 

A  further  test  of  Equation  (136)  is  best  made  by  solving  for  z,  using 
the  values  of  na  and  nr  given  in  Table  XLII.  Sommerfeld  has  carried 
this  computation  throughout  the  range  of  experimental  data  and  finds 
the  value  of  z  constant  for  corresponding  doublets  of  different  elements. 
The  following  mean  values  are  obtained  for  the  different  doublets. 


Doublet  

LI,  2 

M3,  4 

Ml,  2 

A"  5,  6 

N  3,  4 

Nl,2 

z.  . 

350 

825 

13  16 

163 

25.7 

33.9 

The  quantity  z  is  a  measure  of  the  resultant  repulsive  force  of  electrons 
in  the  inner  atom  structure  on  an  electron  at  the  given  level.  To  a  first 
approximation  it  is  numerically  equal  to  the  number  of  electrons  inside 
the  orbit  considered.  The  value  of  z  should  then  increase  progressively 
from  the  K  ring  outward,  being  always  greater  for  levels  of  smaller 


X-RAY  SPECTRA 


211 


energy.  The  above  results  fulfill  this  condition,  viz.  z  (L  1,  2)  <  z 
(M  3,  4)  <  z  (M  1,  2)  <  z  (N  5,  6)  <  z  (N  3,  4)  <  z  (N  1,  2).  The 
values  are  also  of  the  expected  magnitude.  Thus  there  are  10  electrons 
within  the  M  group  for  which  z  =  8  to  13.  That  this  deficiency  re- 
mains the  same  for  different  elements  is  likewise  in  agreement  with  our 
conception  of  the  inner  structure  of  atoms. 

The  second  class  of  doublets  (inaptly  termed  irregular  doublets) 
for  which  V7i  —  Vi/2  =  constant,  are  more  simply  explained.  We 
obtain  directly  from  Equation  (135) : 


(Z  -  z'2)2 


Accordingly 


(137) 


(138) 


That  is,  the  second  type  of  doublet  separation  can  be  ascribed  to  elec- 
trons in  levels  of  the  same  quantum  number  (n  =  na  +  nr)  but  differing 
in  electron  deficiency,  (z'  and  z  distinguish  deficiencies  computed  from 
the  two  types  of  doublets.)  Equation  (137)  is  only  an  approximation 
so  that  z'i  and  z'2  may  differ  considerably  from  the  z'a  computed  from 
relativity  doublets.  However  the  difference  z'2  —  z'i  =  Az'i,2  should 
be  the  actual  difference  in  electron  deficiency  if  as  we  have  assumed 
this  is  the  sole  cause  of  the  frequency  difference.  All  available  data  on 
these  doublets  give  the  following  mean  values. 


L2,  3 

M  2,  3 

NQ,  7 

N4,  5 

AT  2,  3 

A  z'  

1.21 

3.39 

2.3 

4.7 

9 

A  z            

4.91 

9.4 

8.2 

The  lower  row  gives  values  of  A  z  computed  from  differences  in  z  given 
by  relativity  doublets  (z  of  M  1,  2  -  z  of  M  3,  4  =  Az  of  M  2,  3,  etc.). 
The  agreement  is  not  very  close,  but  there  is  great  uncertainty  in  some 
of  the  data  as  well  as  in  the  approximations.  That  the  two  differences 
are  of  the  same  sign  and  magnitude  is  a  fair  justification  of  the  theory. 

We  conclude  that  the  doublets  of  the  first  type;  L  1  and  L  2,  M  1  and 
M  2,  etc.;  all  originate  from  two  orbits  at  the  same  mean  distance  from 
the  nucleus  but  differing  in  ellipticity;  while  apparently  the  pairs  of  the 


212 


ORIGIN  OF  SPECTRA 


second  type;  L  2  and  L  3,  M  2  and  M  3  etc.;  are  orbits  of  the  same  shape 
but  at  different  distances  from  the  nucleus.21  Thus  the  L  3  orbit  is 
inside  of  L  2  so  that  the  electron  deficiency  for  the  latter  orbit  is  in- 
creased by  the  effect  of  electrons  in  L  3.  There  are  then  two  L  levels, 
three  M  levels  and  four  N  levels;  and  at  some  of  these  levels  are  two 
types  of  orbit  differing  in  ellipticity  and  hence  in  energy  because  of  the 
relativity  effect.  This  latter  separation  becomes  negligibly  small  for 
the  limits  of  low  frequency.  The  L  limits  softer  than  L  1  observed  only 
for  light  elements,  do  not  fall  within  the  above  scheme.  These  lines  on 
Figure  35  are  evidently  parallel  and  hence  form  doublets  of  the  second 
type. 

Two  quantum  numbers  na  and  nr  suffice  to  explain  the  doublet 
separation  and,  roughly  at  least,  the  absolute  values  of  the  frequencies  in 
x-ray  spectra.  If  we  attempt  to  find  a  selection  principle  in  the  emission 
spectrum  another  quantum  number  must  be  used.  Wentzel22  has  de- 
veloped a  system  involving  a  third  "grund  quantum  m"23  which  explains 
the  observed  intensity  relations  and  requires  no  change  in  the  other 
quantum  numbers.  As  with  arc  spectra,  transitions  violating  the 
selection  principle  are  improbable  but  not  impossible.  For  details  of 
this  principle  of  selection  the  reader  is  referred  to  the  original  papers. 

The  laws  of  doublet  separation  furnish  the  criteria  for  extrapolating 
the  curves  of  Figure  33  beyond  the  range  of  our  data.  Thus  L  3  on  the 
Moseley  scale  is  parallel  to  L  2.  The  graphs  of  the  relativity  doublets 
converge  as  the  atomic  number  decreases  and  the  five  M  limits  for  light 
elements  approach  three  parallel  lines,  M  1,  2,  M  3,  4,  and  M  5.  As  a 
further  guide  for  extrapolation  we  assume  in  analogy  to  the  L  series 
that  M  1,  2  begins  with  the  ionization  potential  of  argon  at  15.1  volts. 

21  But  see  in  this  relation  Appendix  II. 

22  Reference  10  at  end  of  chapter. 

23  This  is  analogous  to  the  "inner  quantum"  proposed  to  explain  the  selection  principle 
involved  in  doublets  and  triplets  of  arc  spectra.    It  is  found  that,  with  the  exception  of  certain 
very  faint  lines,  x-ray  emission  spectra,  like  arc  and  spark  spectra,  arise  from  transitions 
fulfilling  the  Rubinowicz  selection  principle;    viz.,  the  change  in  na  is  =*=  1  or  0.       But  the 
converse  is  not  true.     All  transitions  fulfilling  this  condition  do  not  appear.     For  instance 
both  Kaz  =  Kl  -  L2  and  Ka?  =  Kl  -  L3  involve  transitions  in  which  An«  =     +  1.   Km 
is  always  a  strong  line  but  Ka.3  is  unobserved  except  in  the  tungsten  spectrum  as  measured  by 
Duane.    Evidently  there  is  in  addition  to  the  Rubinowicz  limitation  another  limiting  factor 
independent  of  the  values  of  na  and  nr.    Wentzel  expresses  the  law  of  selection  as  follows 
Assign  to  the  x-ray  orbits  numbers  m  as  given  below: 


m.. 

K 

LI 

2 

L2 

L3 

Ml 

M2 

M3 

M4 

M5 

ATI 

N2 

N3 

AT4 
3 

N5 

NQ 

N7 
I 

1 

2 

1 

3 

3 

2 

2 

1 

4 

4 

3 

2 

2 

Then  observed  emission  lines  (very  fault  lines  excepted)  arise  in  transitions  for  which  Ana  =  =*=! 
or  0,  Am  =  ±  1 .  At  the  present  time  we  do  not  know  tne  physical  meaning  of  m  or  of  changes 
in  m. 


X-RAY  SPECTRA  213 

It  is  seen  in  Figures  35  and  33  that  critical  potentials  ascribed  by  Kurth 
to  the  N  series,  the  potentials  measured  by  the  authors  for  potassium 
and  nickel,  and  the  molybdenum  point  found  by  Richardson  and  Baz- 
zoni  all  fall  close  to  the  M  1  line.  The  three  higher  potentials  measured 
by  Kurth  are  close  to  M  5  and  the  point  ascribed  by  the  authors  to 
tungsten  falls  on  the  N  1,  2  line. 

Of  the  L  limits  observed  by  Kurth  the  points  for  aluminum  and 
silicon  fall  exactly  on  L  3,  while  for  heavier  elements  measured  potentials 
are  close  to  L  1.  The  fact  that  the  authors  did  not  observe  L  3  is  ex- 
plained by  the  difficulty  in  distinguishing  a  faint  critical  potential  which 
lies  above  a  strong  one.  The  failure  of  Kurth  to  observe  the  L  1,  2 
limit  indicates  that  there  is  a  fundamental  difference  between  soft 
x-radiation  of  solids  and  gases.  We  suggest  the  hypothesis  that  radi- 
ation from  the  outer  x-ray  orbits  is  at  least  partially  suppressed  in 
solids  for  the  same  reason  that  arc  and  spark  spectra  are  entirely  missing. 
In  the  second  row  of  the  periodic  table  the  level  L  1,  2  is  close  to  the 
atom  surface  and  L  3  considerably  below  it.  Hence  in  the  solid  state 
only  L  3  can  freely  emit  radiation.  Beyond  the  second  row  both  L  1,  2 
and  L  3  are  well  within  the  surface  and  radiation  from  the  former  be- 
comes strong.  For  the  same  reason,  the  emission  spectra  observed  by 
Millikan  for  sodium,  magnesium,  and  aluminum  may  belong  to  the  L  3 
series.  The  lines  are  not  then  La  but  possibly  Lfa  or  Z/j84.  If  the  above 
hypothesis  is  admitted  all  serious  discrepancies  in  critical  potential 
measurements  are  removed  and  the  observations  agree  within  experi- 
mental error  with  the  scheme  of  x-ray  limits  computed  from  high  fre- 
quency spectra. 

CONCLUSION 

The  system  of  x-ray  absorption  limits  indicates  the  energy  levels 
within  the  atom  surface  and  must  accordingly  form  the  basis  for  any 
theory  of  atomic  structure.  The  large  number  of  the  absorption  limits 
suggests  the  difficulty  of  the  problem.  There  have  been  several  view- 
points as  to  the  interpretation  of  these  results.  One  is  that  in  any  single 
normal  atom  only  one  type  of  orbit  appears  in  each  K,  L,  M ,  etc.,  level.24 
This  makes  it  possible  to  preserve  the  symmetry  which  it  has  been 
customary  to  ascribe  to  atom  models,  but  unfortunately  this  assumption 
has  other  theoretical  consequences/for  example  fine  structure  of  Klines, 
which  are  impossible  to  reconcile  with  experimental  data. 

We  are  apparently  forced  to  the  conclusion  that  all  the  shapes  of 

«  Reference  11  at  end  of  chapter. 


214  ORIGIN  OF  SPECTRA 

orbits  indicated  by  the  theory  of  relativity-doublets  appear  in  every 
atom.  This  is  the  viewpoint  taken  by  Bohr25  in  his  recently  published 
theory  of  atomic  structure  (see  Appendix  II).  If  we  refer  to  Figure  1 
which  gives  the  possible  shapes  of  orbits  up  to  quantum  number  4  it 
will  be  evident  that  the  simultaneous  existence  of  all  types  of  orbits 
in  a  heavy  atom  results  in  a  very  complicated  structure.  In 
addition  to  this  complexity  due  to  different  shapes  of  orbits  we  have  in 
the  second  type  of  doublets  evidence  of  a  difference  in  size  among  orbits 
of  the  same  shape.  Bohr,  however,  suggests  that  this  frequency  differ- 
ence may  be  due  to  the  existence  of  two  possible  configurations  in  the 
excited  atom  following  the  ejection  of  an  electron  from  one  normal  orbit. 
In  view  of  the  apparent  success  of  the  explanation,  on  the  basis  of  the 
existence  of  two  normal  orbits,  we  must,  at  least  for  the  present,  give  it 
preference  and  conclude  that  absorption  limits  all  correspond  to  energy 
levels  in  the  normal  atom. 

The  test  of  these  theories  will  rest  largely  on  more  extensive  and 
accurate  data  on  absorption  limits.  As  we  have  shown  in  this  chapter, 
the  problem  can  be  approached  both  by  direct  measurements  and  by  the 
computation  of  limits  from  emission  spectra.  The  rapid  progress  of  the 
past  year  in  both  directions  encourages  the  belief  that  a  fairly  complete 
survey  of  the  field  will  be  available  in  the  near  future.  As  to  the  the- 
oretical computation  of  energy  levels,  the  apparent  success  of  previous 
attempts  may  be  misleading.  The  simple  symmetrical  electron  con- 
figurations which  have  been  assumed  in  such  calculations  bear  little 
resemblance  to  the  complicated  structure  indicated  by  experiment. 
The  numerical  agreement  between  computation  and  experiment  over  a 
limited  range  of  x-ray  spectra  (all  published  results  are  limited  to  the 
K  series)  may  be  accidental.  A  complete  solution  of  the  problem  is 
inconceivable  at  the  present  time,  but  a  reconsideration  of  the  assump* 
tions  necessary  for  an  approximate  solution  is  imperative. 

REFERENCES 

1.  Critical  potentials  in  the  x-ray  region. 

Summary:   Webster,  Bui.  Natl.  Res.  Council,  1,  p.  432  (1920). 

L  series  of  tungsten  and  platinum:   Hoyt,  Proc.  Nat.  Acad.  Sci.,  6,  p.  639  (1920). 

M  series:   Ross,  Phys.  Rev.,  18,  p.  336  (1921). 

2.  Soft  x-ray  limits  from  critical  potential  measurements. 

Mohler  and  Foote,  Bur.  of  Standards  Sci.  Paper  No.  425. 
Kurth,  Phys.  Rev.,  18,  p.  461  (1921). 
Richardson  and  Bazzom,  Phil.  Mag.  42,  p.  1015  (1921), 
Hughes,  Phil.  Mag.,  43,  p.  145  (1922). 

3.  Corpuscular  Spectra. 

Rutherford,  Rawlinson  and  Robinson,  Phil.  Mag.,  28,  pp.  277,  281  (1914). 
M.  de  Broglie,  Compt.  rend.,  172,  pp.  274,  527,  and  806;  Compt.  rend.,  173,  p.  527 
(1921). 

«  Reference  12  at  end  of  chapter. 


X-RAY  SPECTRA  215 


4.  Absorption  spectra. 

Summary:   Duane,  Bui.  Natl.  Res.  Council,  1,  p.  384  (1920). 

de  Broglie,  J.  phys.,  p.  161  (1916). 

K  series:  Fricke,  Phys.  Rev.,  16,  p.  202  (1920). 

L  series:  Hertz,  Z.  Physik,  3,  p.  19  (1920). 

M  series:  Stenstrom.  Dissertation,  Lund  (1919). 

Coster,  Z.  Physik,  5,  p.  139  (1921), 

5.  Theory  of  structure  of  x-ray  limits. 

Kossel,  Z.  Physik,  5,  p.  139  (1920). 

6.  Dependence  of  spectra  on  chemical  composition. 

Chlorine:  Lindh,  Z.  Physik,  6,  p.  303  (1921). 
Phosphorus:  Bergengren,  Z.  Physik,  3,  p.  247  (1920). 

7.  Absorption  coefficients  for  x-rays  of  long  wave-length. 

Holweck,  Ann.  phys.,  p.  1  (1922). 

8.  Data  on  emission  spectra. 

Siegbahn,  Jahrbuch  Rad.  u.  Elek.,  13,  p.  296  (1916). 

Duane,  loc.  cit.,  4. 

Stenstrom,  loc.  cit.,  7. 

Hjalmar,  Z.  Physik,  7,  p.  341  (1921). 

Coster,  Z.  Physik,  4,  p.  178  (1921). 

9.  Extension  of  the  range  of  the  diffraction  grating. 

Millikan,  Proc.  Nat.  Acad.  Sci.,  7,  p.  289  (1921). 

10.  Combinations  in  x-ray  spectra. 

Kossel,  Verh.  Deut.  Phys.  Ges.,  16,  pp.  899  and  953  (1914). 

Duane,  loc.  cit.,  4. 

Smekal,  Z.  Physik,  4,  p.  26;  5,  pp.  91  and  121  (1921). 

Dauvillier,  Compt.  rend.,  172,  pp.  915  and  1350  (1921). 

Coster,  Z.  Physik,  6,  p.  185  (1921). 

Wentzel,  Z.  Physik,  6,  p.  84  (1921). 

11.  On  regular  and  irregular  doublets. 

Sommerfeld,  "  Atombau  und  Spektrallinien,"  3d  Edition,  p.  605. 
Hertz,  Z.  Physik,  3,  p.  19  (1920). 

12.  On  the  structure  of  atoms. 

Bohr,  Z.  Physik,  9,  p.  1  (1922). 


Published  since  this  Chapter  was  Written 

On  the  Spectra  of  X-Rays  and  the  (Bohr)  Theory  of  Atomic  Structure.  D.  Coster, 
Phil.  Mag.,  43,  pp.  1070-1107  (1922). 

The  N  Series  Emission  Spectrum  of  Uranium,  Thorium  and  Bismuth.  V.  Dolejsek, 
Z.  Physik,  10,  pp.  129-136  (1922). 


Chapter  X 
Photo-electric  Effect  in  Vapors 

It  is  well  known  that  if  a  solid  or  liquid  metal  is  illuminated  with 
light  of  sufficiently  high  wave  number  v,  photo-electrons  are  emitted.1 
Below  a  minimum  value  of  v  no  emission  takes  place,  but  as  v  is  increased, 
the  emitted  electrons  leave  the  surface  with  increasing  initial  velocity. 
The  metals  in  the  solid  and  liquid  state  are  capable  of  absorbing  the 
•entire  energy  of  the  quantum  of  incident  radiation.  This  energy  is 
conserved  and  is  represented  by  the  kinetic  energy  of  the  emitted  electron 
plus  the  work  required  to  bring  the  electron  through  the  surface  of  the 
metal. 

By  analogy  we  should  expect  a  corresponding  photo-electric  effect 
for  atoms  in  the  vapor  state.  If  the  vapor  is  illuminated  with  light 
of  the  wave  number  corresponding  to  the  highest  convergence  frequency 
in  its  arc  spectrum,  1  s  for  the  alkalis  and  I  S  for  the  metals  of  Group  II, 
a  quantum  of  this  energy  value  should  be  sufficient  to  eject  the  valence 
electron  from  the  atom  with  zero  velocity.  If  the  wave  number  exceeds 
this  minimum  value  we  might  expect  that  the  valence  electron  could 
be  ejected  with  a  velocity  or  kinetic  energy  %  mvz  =  hcv  —  he-  (1  S).  It 
is  conceivable  on  the  other  hand  that  the  atom  would  respond  to  only 
the  single  wave  number  1  S,  the  higher  frequencies  producing  no  effect 
upon  the  valence  electron.  We  shall  see  however  that  there  is  good 
evidence  against  this  latter  hypothesis. 

So  far  the  ordinary  methods  of  measuring  the  photo-electric  effect 
by  observing  the  photo-electric  current  between  two  plates  immersed 
in  the  vapor  which  is  illuminated  by  the  ultra-violet  source  of  light  have 
yielded  very  little  of  a  definite  nature.  The  amount  of  photo-electric 
ionization  has  not  been  sufficient  to  have  enabled  any  of  the  many 
investigators  in  this  field  to  differentiate  it  clearly  from  spurious  effects. 
In  fact  the  very  existence  of  a  photo-electric  effect  should  be  responsible 

i  Hughes,  "Photo-Electricity"  Cambridge  Univ.  Press  (1914).  Supplemented  by  Bull. 
Nat.  Res.  Coun.,  2,  pp.  83-169  (1921). 

216 


216  A 


FIG.  40.  Absorption  of  sodium  vapor  showing  the  presence  of  continuous  absorption 
beginning  at  the  convergence  of  the  principal  series  and  extending  toward  the 
shorter  wave-lengths.  Bright  lines  are  due  to  the  source  of  radiation. 


FIG.  41.  The  lower  spectrogram  shows  the  continuous  absorption  of  sodium  vapor 
beginning  at  the  limit  of  the  principal  series  and  extending  toward  the  shorter 
wave-lengths.  The  upper  spectrogram  shows  the  source  of  radiation  alone. 


PHOTO-ELECTRIC  EFFECT  IN   VAPORS  217 

for  a  spurious  current  consisting  of  electrons  liberated  from  the  electrodes 
by  the  diffused  radiation  from  the  vapor  which  must  be  an  immediate 
consequence  of  photo-electric  ionization.  The  chief  difficulties  encoun- 
tered, however,  have  been  in  the  shielding  of  the  electrodes  from  direct 
and  scattered  radiation  of  the  illuminating  source,  and  the  scattering  by 
impurities,  dust  particles,  condensed  groups  of  atoms,  or  ions,  etc. 

A  probable  exception  to  the  above  statement  is  suggested  by  the 
recent  note  of  Williams  and  Kunz2  who  found  that  caesium  vapor  was 
ionized  by  light  of  wave-length  2530 A  and  that  wave-lengths  longer  than 
X  3130  were  quite  ineffective.  Special  care  was  taken  to  ensure  the 
absence  of  surface  effects.  The  value  of  1  s  for  caesium  is  X  3184. 

The  spectroscopic  consequences  of  a  photo-electric  effect  in  vapors 
are  most  interesting.  If  any  considerable  effect  existed,  and  if  it  re- 
quired for  its  production  radiation  precisely  corresponding  to  the  con- 
vergence wave  number  of  the  principal  series,  we  should  expect  to  find  a 
strong  narrow  absorption  line  at  this  point  in  the  absorption  spectrum 
of  the  normal  vapor.  No  such  phenomenon  has  been  observed. 

On  the  other  hand  if  the  photo-electric  ejection  of  the  valence  electron 
may  be  produced  by  the  absorption  of  radiation  of  any  wave  number 
greater  than  that  corresponding  to  the  highest  convergence  limit  we 
might  expect  to  find  a  well-defined  broad  band  in  the  absorption  spectrum 
terminating  sharply  on  the  long  wave-length  side  at  the  convergence  of 
the  series.  In  fact  this  method  would  immediately  suggest  itself  for  the 
determination  of  series  limits  for  elements  for  which  the  relations  are 
unknown.  This  precise  phenomenon  has  not  been  observed.  We  shall 
see  that  absorption  is  present  but  it  is  not  in  general  very  sharply  defined* 

If  the  ordinary  photo-electric  action  is  possible,  illumination  of  the 
vapor  with  light  of  wave  number  equal  to  or  greater  than  that  of  the 
highest  convergence  frequency  should  produce  ionization.  The  ioniza- 
tion should  be  followed  by  recombination  so  that  with  such  monochro- 
matic stimulation  all  lines  of  the  arc  spectrum  should  be  excited.  The 
authors  have  tried  this  experiment  with  caesium  vapor  obtaining  nega- 
tive results.  However,  from  the  evidence  presented  below  there  is  little 
question  but  that  the  emission  should  be  produced.  It  is  possible  that 
the  effect  is  present,  but  of  insufficient  intensity  to  be  readily  detected. 
The  experiment  is  a  crucial  one  and  worthy  of  extensive  investigation. 

Complete  ionization,  or  certainly  nearly  complete,  may  be  pro- 
duced in  successive  stages  as  shown  by  Fuchtbauer's3  experiments 

2  Phys.  Rev.,  15,  p.  550  (1920). 
'  Physik.  Z.,  21,  pp.  635-8  (1920). 


218  ORIGIN  OF  SPECTRA 

with  mercury  vapor.  As  discussed  in  detail  in  Chapters  IV  and  VI, 
the  mercury  vapor  illuminated  by  light  from  the  mercury  arc  was  found 
to  emit  the  arc  spectrum.  Wood  observed  absorption  of  the  57th  term 
in  the  principal  series  of  sodium.  The  valence  electron  is  accordingly 
ejected  to  the  58  p  orbit  and  the  atom  is  thus  able  to  emit  most  of  the 
arc  lines.  If  the  electron  can  be  ejected  to  the  58  p  orbit  there  is  no 
question  but  that  it  can  be  completely  ejected  by  absorption  of  radiation 
of  slightly  higher  frequency,  for  the  difference  between  the  58  p  orbit 
and  complete  ipnization  is  an  extremely  small  quantity. 

We  have  shown  in  Chapter  IX  that  a  limit  in  x-ray  series  is  sharply 
defined  by  the  edge  of  an  absorption  band.  For  example,  dense  absorp- 
tion begins  abruptly  at  the  K  limit  and  gradually  fades  away  toward 
the  higher  frequencies.  The  reason  that  the  band  is  well  defined  is 
because  the  other  x-ray  orbits  are  occupied.  The  electron  in  the  K-  . 
orbit  can  not  absorb  a  lower  frequency  sufficient  to  displace  it  to  an 
L-orbit,  for  example,  since  the  L-orbits  are  saturated  and  there  is  no 
vacant  place  which  the  ejected  electron  may  occupy.  The  displacement 
must  be  to  a  virtual  orbit  which  is  unoccupied  in  the  normal  atom.  In 
the  case  of  x-rays  these  virtual  orbits  are  so  far  out  that  displacement 
to  any  of  them  amounts  to  complete  ejection  as  far  as  the  energy  or  the 
spectral  frequencies  are  concerned. 

The  case  is  totally  different  with  the  spectroscopic  phenomena 
produced  by  the  valence  electron.  Here  all  orbits  outside  the  normal 
orbit  occupied  by  the  electron  are  virtual  or  unfilled.  The  electron 
may  be  displaced  to  any  of  an  infinite  number  of  virtual  orbits  by  absorp- 
tion of  radiation.  The  main  reason  the  lines  of  the  principal  series  of 
sodium  were  not  detected  by  Wood  beyond  m  =  58  was  because  of 
insufficient  resolution.  The  absorption  is  present  but  the  58  to  oo 
terms  are  all  so  close  together  that  they  appear  as  a  continuous  band 
terminating  at  the  convergence  of  the  series.  Now  if  the  atoms  could 
not  absorb  radiation  of  higher  wave  number  than  this,  that  is  if  there 
were  no  photo-electric  effect,  the  absorption  spectrum  should  terminate 
sharply  at  the  convergence  frequency.  We  would  have  a  dark  band 
from  m  =  58  to  m  —  oo  and  the  clear  bright  background  of  the  con- 
tinuous source  at  the  higher  frequencies.  The  phenomenon  usually 
observed  however  is  an  apparently  continuous  absorption  extending 
from,  say  m  =  58  to  wave-lengths  much  shorter  than  that  corresponding 
to  1  s.  That  is,  the  apparent  band  spectrum  due  to  the  close  linfe  absorp- 
tion joins  on  to  the  true  band  spectrum,  at  wave  numbers  greater  than 
1  s,  and  there  is  no  abrupt  change  in  the  spectrum  at  1  s.  The  band 


PHOTO-ELECTRIC  EFFECT  IN   VAPORS  219 

spectrum  at  wave  numbers  greater  than  1  s  indicates  the  existence  of  the 
photo-electric  effect  in  vapors. 

Under  certain  experimental  conditions  it  is  possible  to  accentuate 
the  amount  of  continuous  absorption  over  that  of  the  line  absorption 
so  that  a  slight  discontinuity  is  observable  at  1  s.  Apparently  one 
condition  for  this  result  is  high  vapor  density.  Figure  40  shows  three 
absorption  spectrograms  for  sodium  vapor  made  from  Professor  Wood's 
original  negatives.  The  higher  terms  of  the  principal  series  show  as 
absorption  lines  on  the  right  half  of  the  figure.  Unfortunately,  the 
bright  lines  from  the  cadmium  spark  used  as  the  continuous  source 
detract  somewhat  from  the  appearance  of  the  prints.  However,  one 
sees  that,  because  of  insufficient  dispersion  and  resolution,  the  lines 
crowd  together  near  the  convergence  forming  what  appears  to  be  band 
absorption.  At  the  point  A  which  marks  the  head  of  the  series  a  genuine, 
continuous  absorption  spectrum  is  present  which  extends  to  the  left 
for  a  considerable  distance  into  the  ultra-violet.  The  point  to  which 
attention  is  specially  directed  is  the  fact  that  the  absorption  is  con- 
siderably more  pronounced  over  the  spectral  region  indicated  by  the 
arrow  than  at  the  head  of  the  series  just  to  the  right  of  the  arrow.  The 
source,  however,  if  photographed  alone,  is  of  uniform  brightness  in  this 
region.  This  illustration  clearly  demonstrates  the  presence  of  the  con- 
tinuous absorption  beginning  at  the  head  of  the  series  and  extending 
toward  the  higher  frequencies,  a  fact  pointed  out  by  Wood4  in  1909. 
In  his  paper  he  states  "  One  point  of  great  interest  noted  with  very  dense 
sodium  vapor  is  the  general  absorption  which  begins  exactly  at  the  head 
of  the  principal  series  and  extends  from  this  point  down  to  the  end  of  the 
ultra-violet.  The  vapor  is  much  more  transparent  to  the  light  between 
the  absorption  lines  than  in  the  region  below  the  head  of  the  series. 
The  head  of  the  series  actually  shows  much  brighter  on  this  account 
than  the  rest  of  the  spectrum  below  it." 

This  is  again  brought  out  by  Figure  41,  a  photograph  made  by  Dr. 
George  Harrison  under  similar  conditions.  Below  the  limit,  the  con- 
tinuous absorption  is  much  greater  than  anywhere  between  the  principal 
series  lines  from  m  =  9  to  the  limit.  The  upper  spectrogram  shows 
the  cadmium  source  alone,  the  intensity  of  which  is  fairly  uniform. 

We  have  found  in  Chapter  VI  that  if  the  vapor  pressure  is  high  an 
appreciable  fraction  of  the  atoms  may  be  excited,  the  valence  electron 
being  maintained  in  the  2  p  orbit  by  absorption  of  the  temporarily 
imprisoned  resonance  radiation.  Hence  for  such  atoms  there  should  be 

«  Astrophys.  J.,  29,  pp.  97-100  (1909). 


220 


ORIGIN  OF  SPECTRA 


a  region  of  continuous  absorption  denned  sharply  on  the  red  side  at  2  p 
or  for  sodium  at  about  X  =  4080.  There  is  an  indication  of  this  at  the 
extreme  left  of  the  illustration.  The  wave-length  concerned,  however, 
lies  outside  the  portion  of  the  spectrogram  here  reproduced.  One 
would  expect  that  if  such  a  continuous  absorption  were  present,  lines 
of  the  subordinate  series  should  be  reversed.  However,  it  is  worthy 
of  note  that  under  the  above  described  conditions  some  continuous 
absorption  may  be  expected  at  2  p  and  at  higher  wave  numbers  such  as 
2  s,  3  d,  3  p,  etc.  This  absorption,  of  course,  will  be  superposed  on  the 
structured  band  spectrum  arising  in  the  molecule  Na2  and  in  general  is 
probably  too  faint  to  be  detected.  Furthermore  the  different  bands 
beginning  at  3  p}  3  d}  2  s,  2  p,  etc.  probably  overlap  and  give  the  appear- 
ance of  a  continuous  stretch  of  faint  absorption. 


O  o 

o  o 


Na 


I    I   I   I  1 


12     13 


19 


19 


Limit 


FIG.  42.     Transmission  of  sodium  vapor  for  radiation  near  the  limit  of  the  principal 

series. 

Holtsmark5  has  made  micro-photometric  measurements  on  the 
transmission  of  a  photographic  negative  throughout  the  region  of  the 
absorption  spectra  of  sodium  and  potassium.  The  photographs  were 
similar  to  those  in  Figures  40  and  41  except  that  lower  vapor  pressure 
was  employed  and  there  was  no  detectable  transition  from  the  line 
absorption  to  the  band  absorption.  The  negatives  were  of  uniform 
density  throughout  this  region.  Figure  42  shows  his  results  for  sodium 
where  the  wave-length  with  increasing  values  toward  the  left  is  plotted 
against  a  function  of  the  intensity  of  the  light  transmitted  by  the  column  of 
vapor. 

s  Physik.  Z.,  20,  pp.  88-92  (1919). 


PHOTO-ELECTRIC  EFFECT  IN   VAPORS 


221 


The  upper  curve  represents  the  observations  on  the  portion  of  the 
spectrum  lying  between  the  lines,  the  ordinal  numbers  of  which  are 
indicated  below.  The  lower  curve  from  line  14  to  the  head  of  the 
series  represents  the  photometric  measurements  made  on  the  absorption 
lines  themselves.  The  points  to  the  right  lying  at  higher  frequencies 
than  the  head  are  due  to  the  continuous  absorption.  One  notes  that 
the  lower  curve  shows  no  abrupt  change  in  passing  the  head  of  the 
series.  The  line  absorption  goes  over  into  the  band  absorption  without 
discontinuity.  However,  the  comparison  must  be  made  with  the  upper 
curve.  If  it  were  not  for  the  line  absorption  crowding  together,  making 
measurements  between  the  lines  impossible  near  the  head,  we  would 
find  the  intensity  curve  following  the  course  of  the  dotted  line  with  a 
sharp  break  at  the  head.  This  is  identically  the  type  of  curve  char- 


Limit 

FIG.  43.     Transmission  of  potassium  vapor  for  radiation  near  the  limit  of  the  principal 

series. 

acteristic  of  x-ray  absorption  limits.  The  only  reason  it  is  so  difficult 
to  detect  in  optical  spectra  is  because  the  effect  is  in  general  obliterated 
or  greatly  reduced  by  the  line  absorption  which  is  absent  with  x-rays. 

Figure  43  shows  similar  results  with  potassium.  The  upper  curve 
refers  to  the  intensity  between  the  lines  and  the  lower  curve  to  the 
intensity  in  the  continuous  band  beginning  with  the  head  of  the  principal 
series.  A  sharp  break  appears  at  v  =  Is,  the  limit. 

We  have  mentioned  that  if  continuous  absorption  is  present  at 
the  head  of  the  principal  series  we  should  also  find  it  at  the  head  of  the 
subordinate  series  when  a  sufficient  number  of  atoms  are, excited,  having 
the  valence  electron  in  the  2  p  ring.  Thus  with  hydrogen,  while  the 
true  photo-electric  absorption  of  the  normal  vapor  begins  at  the  head 
of  the  Lyman  series  in  the  far  ultra-violet,  that  of  the  excited  gas  should 


222  ORIGIN  OF  SPECTRA 

begin  at  the  head  of  the  Balmer  series  and  extend  toward  the  shorter 
wave-lengths.  In  certain  hydrogen  stars  as  discussed  in  Chapter  VII 
an  appreciable  fraction  of  the  hydrogen  atoms  have  the  electron  in  the 
second  orbit.  Such  stars  should  show  a  continuous  band  absorption 
limited  on  the  less  refrangible  side  at  v  =  %  N-R  or  X  =  3646. 

Huggins6  observed  that  "a  characteristic  feature  of  white-star 
spectra  consists  in  the  rather  sudden  fall  of  intensity  of  the  continuous 
spectrum  at  about  the  place  of  the  end  of  the  series  of  dark  hydrogen 
lines.  The  spectrum,  much  enfeebled,  continues  to  run  on  without  any 
further  sudden  enfeeblement  until  it  is  stopped  by  the  absorption  of  our 
atmosphere.  This  fall  of  intensity  is  most  truly  appreciated  by  compar- 
ing the  brightness  of  the  continuous  spectrum  in  the  narrow  intervals 
between  the  last  few  hydrogen  lines  with  the  brightness  of  the  continuous 
spectrum  a  little  beyond  the  termination  of  the  series  of  lines." 

Hartmann7  has  made  a  systematic  photometric  study  of  several 
hydrogen  stars  and  from  numerous  measurements  concludes  that  there 
is  a  general  absorption  from  the  head  of  the  Balmer  series  to  about 
X  3400. 

Horton  and  Davies  were  led  to  conclude  from  their  experiments  on 
ionization  potential,  that  helium,  excited  by  20.4  volt  electronic  im- 
pact, may  be  ionized  by  absorption  of  the  21.2  volt  radiation  of  helium. 
If  this  observation  be  correct  it  indicates  a  photo-electric  action  analogous 
to  that  described  for  hydrogen. 

In  conclusion  we  find  that  while  attempts  to  detect  a  photo-electric 
effect  in  vapors  by  electrical  means  have  not  yielded  satisfactory  results, 
the  spectroscopic  evidence  for  the  existence  of  the  effect  is  perfectly 
definite  and  that  the  phenomenon  takes  place  precisely  as  predicted  by 
the  quantum  theory  of  absorption. 

•  "An  Atlas  of  Representative  Spectra,"  p.  85. 

*  Physik.  Z.,  18,  pp.  429-32  (1917). 


Chapter  XI 
Determinations  of  h  Involving  Line  Spectra 

Birge1  has  summarized  up  to  July,  1919,  the  determinations  of 
Planck's  constant  h  by  seven  independent  methods  and  has  concluded 
that  the  most  probable  value  is  h  =J).554-JQ-27  erg  sec.  This  is  the 
number  employed  for  computation  throughout  this  book. 

Probably  the  most  accurate  means  for  the  determination  of  h  is  by 
the  application  of  the  quantum  relation  to  general  x-radiation.  Duane's2 
most  recent  value  by  this  method  gave[6.556  •  10~27.  We  shall,  however, 
confine  our  discussion  to  the  methods,  less  precise  at  present,  which 
involve  the  spectroscopic  measurement  of  frequencies  belonging  to  line 
series,  for  example,  the  limit  of  a  principal  spectral  series,  an  x-ray 
limit,  or  a  particular  emission  line. 

There  are  three  direct  means  for  this:  (1)  by  the  x-ray  method  in- 
volving the  correlation  of  the  critical  potential  required  to  excite  an 
x-ray  series  and  the  wave  number  or  frequency  of  the  limit  of  the  series 
as  determined  by  the  absorption  spectrum;  (2)  by  use  of  the  empirically 
determined  value  ,of  the  Rydberg  constant  Nw  in  Equation  (7) ;  (3)  by  N 
measurements  of  ionization  and  resonance  potentials  and  the  correspond- / 
ing  spectral  wave 'numbers,  employing  the  quantum  relation  h&v  — 
*V'1&. 

CHARACTERISTIC  X-RAYS 

Table  XLIII  summarizes  typical  data  on  the  determination  of  h 
by  this  method.  We  have  seen  in  Chapters  I  and  IX  that  as  the  kinetic 
energy  of  the  impacting  electron  is  increased  by  raising  the  accelerating 
voltage,  a  critical  value  is  reached  which  is  just  sufficient  to  produce 
complete  ejection  of  an  electron  from  an  x-ray  ring.  Because  of  this 
ejection,  for  example  from  the  X-ring,  a  vacant  space  is  created  into 
which  an  L-electron  falls  with  the  resulting  emission  of  Ka  etc.  One, 
accordingly,  observes  the  minimum  potential,  V,  at  which  the  K  lines 

*  Phys.  Rev.,  14,  pp.  361-8  (1919),  see  also  Ladenburg,  Jahrbuch  Rad.  u.  Elek.,  17,  p.  93 
(1920). 

2  Duane,  Palmer  and  Chi-Sun-Yeh,  J.  Opt.  Soc.  Am.,  5,  pp.  376-87  (1921). 

223 


224 


ORIGIN  OF  SPECTRA 


are  excited.     This  is  correlated  with  the  absorption  limit  X  by  the  quan- 
tum relation : 


h 


108 


5.309  -10-23  FXCOT, 


(139) 


where  e  =  4.774 -IQ-10  e.s.u.  and  c  =  2.9986  -1010  cm/sec.,  the  wave- 
length X  being  expressed  in  cm. 

There  is  little  doubt  but  that  the  method  is  capable  of  far  greater 
precision  than  is  indicated  by  the  values  in  Table  XLIil.  The  technique 
has  not  been  developed  because  of  the  more  satisfactory  method  involv- 
ing the  general  x-radiation.  The  recent  value  for  aluminum  by  Holweck 
was  obtained  in  a  different  manner  as  described  on  page  202. 

TABLE  XLIII 

DETERMINATION  OF  h  BY  CHARACTERISTIC  X-RAYS 


Element 

Limit 

X-HFcm 
Duane 

Minimum 
voltage 

h-W 

Investigator 

Mo 

K 

.6184 

19200 

6.30 

Wooten  * 

Rh  

K 

.5330 

23300 

6.59 

Webster  ** 

Pd  

K 

.5075 

24000 

6.47 

Wooten  * 

W 

K 

.1781 

70-80000 

6.7 

Hull  and  Rice  t 

Pt 

Li 

1.070 

11450 

650 

Webster  and  Clark  ff 

Al  

L, 
K 

.932 
7.947 

13200 
1555 

6.54 
6.56 

Webster  and  Clark 
Holweck,  cf  .  Table  40 

*  Phys.  Rev.,  13,  pp.  17-86  (1919). 

**  Phys.  Rev.,  7,  pp.  599-613  (1916). 

t  Proc.  Nat.  Acad.  Sci.,  2,  pp.  265-70  (1916). 

tt  Phys.  Rev.,  9,  p.  571  (1917). 


THE  RYDBERG  NUMBER 

Equation  (7),  derived  theoretically,  in  which  N^  denotes  the  Ryd- 
berg  series  constant  for  an  element  having  a  nucleus  of  infinite  mass, 
gives  directly  for  h: 


(140^ 


c  (e/m)  N 


GO 


The  relation  between  N^  and  N  for  a  nuclear  mass  M  is  expressed  by 
Equation  (8).     From  empirically  determined  values  of  NH  and  A7He 


DETERMINATIONS  OF  h  225 

obtained  by  a  consideration  of  the  lines  of  hydrogen  and  ionized  helium 
respectively,  Paschen3  found  that 

#00  =  109737.11. 

This  value  may  be  readily  verified  by  use  of  Equations  (8)  and  (10), 
the  independent  determinations  with  hydrogen  and  helium  agreeing 
to  the  last  significant  figure  given. 

The  value  of  e/m  may  be  also  derived  from  observations  on  the 
wave-lengths  of  the  hydrogen  and  helium  lines  as  shown  by  Equation 
(12).  This  optically  determined  quantity  is  e/m  =  5.343  -1017  e.s.u./g. 
Substituting  these  values  in  Equation  (140)  we  find: 

h  =  6.53  -10-27  erg  sec., 

where  the  controlling  error  should  be  in  the  magnitude  of  the  elementary 
charge  and  in  e/m. 

lONIZATION   AND    RESONANCE   POTENTIALS 

If  we  use  the  values  of  the  ionization  and  resonance  potentials  listed 
in  Tables  X,  XI  and  XXIV  and  the  corresponding  wave  numbers  which 
are  known  with  high  precision  from  spectroscopic  determinations,  we 
may  employ  the  quantum  relation  to  obtain  a  value  for  h  as  follows  : 


h  _  Ve'  10*  _.  f 

~~#v          L88347 

The  authors,  in  1920,  summarized  their  own  data,  to  that  date,  which 
included  twenty  independent  points  on  various  elements,  each  of  course 
a  mean  of  a  large  number  of  measurements.4  Equal  weight  was  given 
to  each  observation  with  the  resulting  mean  h  =  6.55  -10~27.  Since 
then  more  points  have  been  obtained  by  ourselves  and  others.  We  have 
plotted  in  Figure  44  thirty-three  values,  listed  in  the  tables  referred  to, 
for  which  the  spectroscopic  frequencies  are  known.  Assigning  equal 
weight  to  each  determination  the  mean  value,  h  =  6.544  ±  0.015  prob- 
able error,  is  obtained. 

There  is  no  doubt  but  that  this  method  properly  carried  out  will 
yield  results  of  a  precision  comparable  to  that  obtained  by  the  best  of 
the  other  methods.  Up  to  the  present  time  the  primary  object  has  been 
to  determine  critical  potentials  for  a  large  number  of  elements  and  little 
attention  has  been  given  to  the  conditions  favorable  for  the  measurement 
of  h.  For  example,  a  metal  like  calcium  which  can  be  handled  only  with 

3  See  Chapter  I.  Computed  from  Paschen's  values  on  NH  and  NHft,  cf.  Ann.  Phys.  50, 
p.  935  (1916). 

«  Foote  and  Mohler,  J.  Opt.  Soc.  Am.,  2-3,  pp.  96-9  (1919). 


226 


ORIGIN  OF  SPECTRA 


difficulty,  is  of  little  service  in  this  regard.    By  using  the  recently 
developed  refinements  in  the  measurement  of  critical  potentials  and  by 


10 


8 


CD 


0  20,000  40,000  60,000  80,OOO 

ti 
FIG.  44.     Determination  of  h  by  ionization  and  resonance  potentials. 

employing  a  method  of  magnetic  dispersion  to  produce  a  univelocity 
stream  of  electrons,  high  precision  in  h  may  be  expected  with  an  easily 
controlled  vapor  such  as  mercury. 


Appendix  I 
Computational  Data 

TABLE  XLIV 

VALUES  OF  NUCLEAR  DEFECT,  sn,  (Cr.  Equation  44) 


n 

sn 

n 

Sn 

1 

0 

14 

6.159 

2 

0.250 

15 

6.764 

3 

0.577 

16 

7.379 

4 

0.957 

17 

7.991 

5 

1.377 

18 

8.624 

6 

1.828 

19 

9.27 

7 

2.305 

20 

9.92 

8 

2.805 

21 

10.57 

9 

3.328 

22 

11.24 

10 

3.863 

23 

11.92 

11 

4.416 

24 

12.60 

12 

4.984 

25 

13.29 

13 

5.565 

26 

13.98 

227 


228 


ORIGIN  OF  SPECTRA 


TABLE  XLV 
NUMERICAL  MAGNITUDES 


h 

6.554  -10-*7 

e 

4.774-  10~10 

7T 

3.142 

m0 

8.93  -10-28 

h* 

4.295  -10-63 

e* 

2.279  -10-19 

T2 

9.870 

mo2 

7.97  -10-63 

h3 

2.815  -10-79 

e3 

1.088  -10^8 

7T3 

31.01 

Nxhc 

2.157  -10-11 

h* 

1.845  -10-106 

e' 

5.194-  10-38 

7T4 

97.42 

h2 

6.04  -10^8 

S-j^mo 

*. 

1.209  -10~131 

e6 

2.48  -10-47 

V~, 

1.772 

e 
mo 

5.34  -1017 
e.s.u./g. 

c 

2.9986-  10™ 

2  ire* 

a2 

5.31-  10-5 

#06 

109737-11 

he 

Voits  =  y  =  ^=^. 

e  \A         XA 
Volts  =  V  =  — 10~8  =  1.2345 


•(\A  measured  in  Angstroms) 
v  •  10~4      (v  =  wave  number) 


v  =  r —  =  — —        (wave-lengths  reduced  to  vacuo) 

Acm  A.4. 

v  =  8100  V          v  =  frequency  =  c  v 
Number  molecules/gm  mol  =  6.06  •  1023 
Number  molecules/cm3  at  760  mm  and  0°  C  =  2.705 -1019 
Faraday  constant  =  96500  ±  10  coulombs 
One  20°  cal.  =  4.183 -107  ergs 
(20°  cal./gm  mol)  -r-  23070  =  Volts/molecule 
(Kg  cal./gm  mol)  -T-  23.07   =  Volts/molecule 
Ergs  =  1.592 -10-12  X  volts 
Ergs  =  1.965 -10-16^ 
v  =  5.088  X  ergs-1016 

Gas  constant  =  R  =  8.315 -107  ergs/deg.  C.      (referred  to  mol  of  gas) 
=  1.985       g  cal./deg.  C.      (referred  to  mol  of  gas) 
Kinetic  energy  of  translation  of  av.  molecule  at  0°  C  =  5.62- 10~14  ergs    ^ 

/V~ 

Velocity  of  singly  charged  ion  =  1.389-106  y  -r:  cm/sec:  (V  =  volts,  M  =  mo- 
lecular weight) 

Root  mean  square  velocity  =  C  =  1.579  •104\/77/M  cm/sec.  (T  =  abs.  temp., 
M  =  mol.  wt.) 

Mean  free  path  of  electron  in  gas  =  I/TT  r2n  cm.  (r  =  radius  of  gas  molecule, 
n  =  number  of  molecules /cm3) 


U\ 


APPENDIX  I  229 

VELOCITIES  OF  ELECTRONS,  IONS  AND  MOLECULES 

(Explanation  of  Figure  45) 

The  relation  between  the  molecular  weight,  M,  of  an  ideal  gas,  its 
absolute  temperature  T,  and  the  root  mean  square  velocity  C  of  a  mole- 
cule is  given  by 

C  =  VZ  RT/M      =  1.579-10*  VTjM  cm/sec., 

where  R  is  the  gas  constant,  8.315-  107  ergs/0  C. 

I.  To  obtain  C,  knowing  T  and  M:   Lay  a  straight-edge  from  M  on 
scale  (1)  to  T  on  scale  (4).     At  the  intersection  with  scale  (2)  read  C 
in  cm/sec.     Example:    The  helium  atom  (M  =  4)  at  a  temperature  of 
20°  C  (T  =  293°  K)  has  a  root  mean  square  velocity  1.38-105  cm/sec. 

II.  To  obtain  the  thermal  velocity  of  an  electron:    Lay  a  straight-edge 
from  the  electron  point  on  scale  (1)  to  T  on  scale  (4).     Read  its  inter- 
section with  scale  (2)  and  multiply  by  100  (since  a  mass  104  times  too 
large  has  been  used). 

The  relation  between  v,  the  velocity  of  a  singly  charged  ion  of  mass 
m,  and  the  voltage  V  producing  that  velocity,  is  : 

i  mtf  =  eV  •  108/c  =  eF/300, 

also  e/m  =  f/'M,  where  /  =  96500  coulombs  =  1  faraday  =  9650c  e.s.u. 
of  charge. 

.'.  v  =  1.389  •  106  VVjM  cm/sec. 

III.  To  obtain  v  for  a  simply  charged  ion,  knowing  V  and  M  (where 
V  lies  between  0.1  and  100  volts)  lay  a  straight-edge  from  M  on  scale 
(1)  to  V  on  scale  (6).     At  the  intersection  with  scale  (3)  read  velocity 
of  ion  in  cm/sec. 

IV.  To  obtain  the  velocity  of  an  electron  after  acceleration  by  a  voltage 
V  lying  between  0.1  and  100:     Lay  a  straight-edge  from  the  electron 
point  on  scale  (1)  to  V  on  scale  (6),  read  its  intersection  with  scale  (3) 
and  multiply  by  100  (since  a  mass  104  times  too  large  has  been  used). 
Example:  A  4.9  volt  electron  has  a  velocity,  100-1.32-106  =  1  .32-10* 
cm/sec. 

(If  the  voltage  V  is  greater  than  100,  proceed  as  follows.) 

V.  To  obtain  v  for  an  ion,  knowing  V  and  M:  Proceed  as  in  III, 
using  1/100  of  the  voltage  on  scale  (6),  and  multiply  the  result  by  10. 
Example  :     The  velocity  of  a  singly  charged  mercury  atom  (M  =  200)  , 
after  falling  through  110  volts,  is  10  times  1.03  -105  =  1.03  -106  cm/sec. 


230  ORIGIN  OF  SPECTRA 

VI.  To  obtain  v  for  an  electron,  "knowing  V  and  M.  Lay  a  straight- 
edge from  the  electron  point  on  scale  (1),  to  1/100  of  the  voltage  on 
scale  (6).  Read  the  intersection  with  scale  (3)  and  multiply  by  1000. 
Example:  A  110  volt  electron  has  a  velocity  1000  times  6.2 -105  =  6.2- 
108,  change  of  mass  with  velocity  being  left  out  of  account. 

Scales1  (5)  and  (6)  give  directly  the  wave-length  of  the  quantum 
emitted  by  an  atom  when  it  collides  inelastically  with  a  V  volt  electron. 

The  reader  will  be  able  to  work  out  many  other  combinations.  The 
principle  of  the  chart  is  simple.  It  will  be  noted  that  all  the  scales 
have  a  similar  logarithmic  spacing.  Scales  (1),  (2),  (4)  belong  together, 
as  do  also  scales  (1),  (3),  (6),  scale  (1)  doing  double  service  to  save  space. 
We  have,  for  example : 

log  C  =  log  (1.579  -104)  +  J  log  T  -  1  log  M. 

In  using  the  chart  as  in  I,  we  subtract  graphically  ^  log  M  from  \  log  T. 
The  graphical  addition  of  log  (1.579 -10*)  has  been  cared  for  by  shifting 
the  origin  of  scale  (2)  with  respect  to  the  origins  of  (1)  and  (4).  Similar 
remarks  hold  true  for  the  relation  between  v,  V,  and  M . 

The  chart  cannot  be  applied  directly  to  multiply  charged  ions,  but 
it  is  easy  to  read  the  results  for  a  singly  charged  ion  and  to  multiply  by 
the  appropriate  factor  as  found  from  the  formulae  given  above. 

The  authors  are  indebted  to  Mr.  W.  H.  Holden  for  suggesting  the 
usefulness  of  such  charts  and  to  Mr.  Arthur  E.  Ruark  for  preparing  this 
particular  arrangement.  If  the  reader  has  occasion  to  do  much  rough 
computational  work  of  this  character,  he  will  find  that  the  few  moments 
spent  in  studying  the  principle  of  this  chart  will  be  amply  repaid. 


230  A 


4 

Electron, 
6    .000546.  * 
7 
8 

?o 


•12 


40    3 

o> 

50  "O 

60  ^ 

70 

80 

9O 

100 

-120 
-HO 
-160 
180 
-200 


-300 

•400 
•500 
•600 
•700 
•600 
•900 


3 

S 

'o 


o 
_o 

^ 

! 


C3 
tt 

I 

O 


1.4- 
1.2- 


-1.2 


2- 
U 

1.6- 
1.4- 
12- 


2 

18- 
l.( 


10 

9 
•8 

•7 

6 


-2 

1.8 

1.6 

1.4 

•1.2 


,«e 


•10 

::-j 


900( 

aoc 

7000 
6000- 
5000- 

4000 
3000 


2000' 
1800- 


i; 

1000- 
aj    900' 
*5     800- 
O      J^     700- 


3 


•2 

1.6 
•1.6 

•1.4 
•1.2 

-10s 

•9 

•8 

•7 

•6 

•5 

-4 


•2 

•1.9 
-1,6, 


£ 


O 
O 

I 


< 

c 

*0> 

^    200 
Q>"         " 

u       i< 

2    M 

2         M 

|K 

o> 

U-       80- 


co- 
st 

40- 
30- 


20- 
M 

16- 


t: 

I    7- 


10- 


90 
•80 
•70 
•60 
•50 

•40 

•30 


-20 
.8 

16 
-14 
-\2 

-1O 
9 
•O 
•7 
•6 


•2 
1.8 
-L6 
1.4 
•12 

1 

•0.9 
•OB 

a7 
•0.6 

•as 

•0.4 
•0.3 


.2 

•0.18 
-0.16 

1.14 


FIG.  45.     Velocities  of  electrons,  ions  and  molecules. 


APPENDIX  I 


231 


£**. 

s  a 


g 


m 
«§ 


PQ   en. 
in 


CM 


-<    05 


S 


Si 


S3 


l 


i 


_  • 


5 


Ml 


S 


i 


(S  P5 


LU 


in 


<M   O 


8? 


y  (N 
00  CD 
tf5  <^ 


H  00 


0  ro 


£  ^ 
H  oo 


i^  ro 

(O    CD 


P  •« 

§OJ 
(O 


,0 

H   04 
in  O) 


Appendix  II 
Bohr's  Theory  of  Atomic  Structure1 

The  system  of  electron  configurations  in  non-hydrogen  types  of  atom 
recently  proposed  by  Bohr  is  a  radical  departure  from  the  atomic  models 
heretofore  suggested.  As  yet  none  of  the  mathematical  steps  in  the 
development  of  the  theory  have  been  published,  and  hence  most  of  the 
following  outline  will  appear  purely  empirical. 

In  reality,  however,  the  new  theory  is  an  attempt  to  avoid  arbitrary 
assumptions  as  to  atomic  structure.  Bohr  postulates  that  the  normal 
electron  configuration  about  a  nucleus  Ze  must  be  such  as  would  result 
by  adding  Z  electrons,  one  at  a  time,  to  the  structure,  so  that  each 
electron  occupies  that  orbit  which  is  most  stable  with  respect  to  the 
nucleus  and  previously  bound  electrons.  This  excludes  the  possibility 
of  either  a  ring  configuration  or  of  groups  of  electrons  in  polyhedral 
symmetry.  The  ring  structure  appears  to  require  the  simultaneous 
binding  of  all  the  electrons  in  the  symmetrical  group.  On  the  basis 
of  the  new  theory  each  electron  will  occupy  a  separate  orbit  and  will  be 
to  a  large  extent  independent  of  other  electrons  in  the  same  group. 

We  can  investigate  directly  only  the  last  stages  of  the  atom  building 
as  shown  in  arc  and  spark  spectra.  A  convenient  approach  to  the 
problem  of  the  earlier  steps  in  the  formation  of  a  heavy  atom  is  found  in 
a  study  of  successive  elements  in  the  periodic  table.  The  stages  are 
marked,  by  the  periodic  appearance  of  groups  of  electron  orbits  of 
increasing  total  quantum  number,  and  by  the  subdivision  of  each 
group  into  orbits  of  different  degrees  of  ellipticity. 

Periods  in  atom  structure  correspond  to  intervals  between  rare 
gases  in  the  periodic  table.  Table  XL VIII  shows  the  electron  distribu- 
tion in  these  gases  and  at  certain  intermediate  stages.  Table  XLIX 
gives  the  transitions  in  structure  between  the  stages  shown  in  Table 
XL VIII.  The  following  paragraphs  are  in  explanation  of  the  system 
outlined  in  the  tables. 

*Z.  Physik,  9,  p.  1  (1922). 

232 


APPENDIX  II 


233 


To  picture  the  different  shapes  of  orbits  it  will  be  helpful  to  refer  to 
Figure  1,  Chapter  I,  which  illustrates  possible  types  of  hydrogen  orbits 
to  quantum  number  4.  These  are,  at  least  to  a  first  approximation,  the 
types  of  orbit  appearing  in  heavier  atoms,  the  essential  difference  being 
that  only  one  orbit  is  occupied  in  this  figure  while  in  general  as  many 
orbits  are  occupied  as  there  are  electrons  in  the  atom. 

First  Period.  —  The  theory  of  the  hydrogen  atom  remains  unchanged 
and  its  line  spectra  show  us  the  separate  steps  in  the  binding  of  the  first 
electron.  The  final  state  is  a  circular  orbit  of  quantum  number  1. 
The  binding  of  the  first  electron  in  helium  or  any  heavier  element  is 
similar  except  that  the  factor  Z2  enters  into  the  energy  equations. 


TABLE  XLVII 
QUANTUM  NUMBER  NOTATION 


Total 
Quantum 
n 

Azimuthal 
Quantum 
na 

Radial 
Quantum 
nr 

Bohr 
Notation 
nna 

Shape  of 
Orbit 

1 

1 

0 

li 

circle 

2 
2 

2 
1 

0 

1 

22 
2i 

circle 
ellipse 

3 
3 
3 

3 
2 
1 

0 

1 

2 

33 
32 
3i 

circle 
ellipse 
ellipse 

The  introduction  of  the  second  electron  marks  the  departure  from 
former  viewpoints.  In  the  normal  atom  the  two  electrons  are  each  in 
one  quantum  orbits  (circles  to  a  first  approximation)  the  planes  of 
which  make  with  each  other  an  angle  of  120°.  (See  Chapter  III,  section 
on  helium  and  Figure  11.)  This  configuration  (I  of  Table  XLVIII) 
remains  unchanged  for  the  first  two  electrons  in  all  heavier  elements. 

It  is  assumed  that  for  any  further  additions  to  the  atom  structure 
one  quantum  orbits  are  no  longer  possible.  With  groups  of  higher 
quantum  number,  we  will  have  the  appearance  of  sub-groups  differing 
in  orbital  ellipticity.  A  notation  is  used  by  Bohr  which  is  more  con- 
venient in  this  connection  than  specification  of  azimuth  and  radial 
quantum  number;  viz.,  total  and  azimuth  numbers,  as  shown  in  Table 
XLVII. 


234 


ORIGIN  OF  SPECTRA 


TABLE  XLVIII 
STAGES  IN  THE  BUILDING  OF  ATOMS  DISTRIBUTION  OF  ELECTRONS  IN  SUB-GROUPS 

Quantum  Numbers  of  Sub-groups 

€ 

«i 

' 

1 

fl 
| 

"p 

3 

cr 

1 

bO 

1 
| 

s 
>< 

1 

1 

.a 

1 
a 

i 

o 

eS 

•3 

a 

3 

I 

-z 
s 

£ 

3' 
a 

w 

i 

00 

1 

>. 

i 

5 

•B 

EO 

1 

* 

* 

. 

10 

coco 

0 

.5 

TJ-  CO  CO 

tS 

•^f  CO  CO 

j 

00  00 

s 

n 

CO  CO  00  00 

(M  CO 

* 

^  CO  CO  00  00 

** 

4 

rP  CO  CO  00  00 

COI> 

CO 

*«»««** 

5 

•I 

CO 

•^  CO  CO  CO  CO  CO  CO 

(M  CO 

CO 

T^  CO  CO  CO  CO  CO  CO 

22 

* 

—-  — 

1—  1 

H^ 

* 

*^-*-***.^ 

(M  CO 

- 

—  —  — 

w 

Element 

*        *        * 

^-i           03          -^ 

0      ^     ^ 

4 

J  g| 

^                ^ 

APPENDIX  II  235 

Second  Period.  —  In  normal  lithium  the  third  electron  is  in  a  two 
quantum  elliptical  orbit  2i.  The  binding  process  is  seen  in  the  arc 
spectrum.  In  the  three  following  elements  the  additional  electrons 
likewise  fall  in  2i  orbits.  We  must  assume  that  these  have  a  space 
configuration  symmetrical  with  respect  to  each  other  and  to  the  two 
orbits  of  the  helium-like  sub-structure. 

Additional  electrons  in  nitrogen,  oxygen,  fluorine  and  neon  fall  in  22 
circular  orbits.  The  neon  structure  (II,  Table  XL VIII)  must  be  excep- 
tionally stable  and  symmetrical  and  represents  the  configuration  of  the 
first  ten  electrons  in  all  heavier  elements. 

Third  Period.  —  In  the  following  row  of  the  periodic  table  3i  and  82 
orbits  are  added  to  the  neon  sub-structure  in  an  order  similar  to  the 
building  of  the  two  quantum  group  in  the  second  period.  The  binding 
of  the  eleventh  and  twelfth  electrons  gives  the  line  spectra  of  sodium 
and  magnesium.  The  period  is  closed  with  the  stable  argon  structure 
III.  However,  the  outer  structures  of  argon  and  heavier  rare  gases  are 
not  completed  groups,  and,  unlike  the  helium  and  neon  structures,  these 
configurations  appear  in  the  sub-structure  of  only  a  few  elements. 

Fourth  Period.  —  Potassium  and  calcium  have  4i  orbits,  giving  them 
properties  like  sodium  and  magnesium,  but  with  further  increase  in  the 
nuclear  charge  a  new  type  of  transition  appears.  The  33  orbits  become 
more  stable  than  4i,  so  that  successive  electrons  are  added  to  the  sub- 
structure III,  in  an  order  not  yet  determined,  until  the  three  quantum 
group  is  completed  as  in  III'.  This  latter  configuration  does  not  occur 
alone  in  any  element,  but  is  the  sub-structure  of  the  elements  copper  to 
krypton.  These  have  in  addition  to  III',  4i  and  42  orbits  similar  to 
those  of  the  superficial  groups  in  the  second  and  third  periods. 

Fifth  Period.  —  This  period  is  built  in  a  manner  analogous  to  that 
of  the  fourth.  The  5i  orbits  give  to  rubidium  and  strontium  the  char- 
acteristic properties  of  the  alkalis  and  alkali  earths,  respectively,  and 
then  ten  electrons  are  added  to  the  krypton  sub-structure  IV,  producing 
the  structure  IV'.  From  silver  to  xenon  the  eight  electrons  of  the  5i 
and  52  orbits  are  added  to  furnish  the  structure  V  of  xenon. 

Sixth  Period.  —  Beyond  caesium  and  barium  there  is  a  more  exten-. 
sive  change  in  the  sub-structure.  First  the  four  quantum  group  is 
completed  by  the  addition  of  fourteen  electrons  (the  rare  earths)  and  then 
ten  electrons  are  added  to  the  five  quantum  group  to  complete  the 
sub-structure  V.  From  gold  to  niton  eight  electrons  in  61  and  62  orbits 
are  added  to  form  a  characteristic  rare  gas  structure  VI. 

Seventh   Period.  —  After  niton   another  long  period   is   initiated. 


236 


ORIGIN  OF  SPECTRA 


<NCO 

4- 

—  ~ 


(Nrf 


OHH 


coco 

CO'* 


4- 


UhH 


<NCO 


fflt-H 


<N  (M 

4- 


coco 


4- 


H- 


3  c 


•a 


1C  CO 

4- 


«£: 


1.1 


•f 


COCO 

4- 


COIN 
bC 


CO  1-1 


H- 


csa 


03 


Sfc 


COIN 


COIN 

4- 


«O^H 

4- 


4- 


il 


SCO 
^ 

IJ 


£§=§.-§ 

«8  g  °.o 


2     g 


APPENDIX  II  237 

Radium  contains  two  electrons  in  7i  orbits.  Other  transitions  cannot 
be  specified.  The  fact  that  no  elements  beyond  uranium  are  known  is 
explained,  not  by  any  property  of  the  electron  configuration,  but  by  the 
instability  of  heavy  nuclei,  as  evidenced  by  their  radio-activity. 

We  will  review  briefly  some  of  the  properties  of  the  new  Bohr  atoms 
which  can  be  tested  by  experiment. 

X-ray  Spectra.  —  The  evident  interpretation  of  the  origin  of  x-ray 
series  on  the  basis  of  the  above  outlined  atomic  structure  is  that  the 
K,  L,  M,  etc.,  spectra  originate  in  the  groups  of  orbits  of  total  quantum 
number  1, 2, 3,  etc.,  respectively,  and  that  each  series  starts  with  the  rare 
gas  in  which  the  corresponding  group  of  orbits  first  appears.  This  is  in 
exact  accord  with  the  conclusions  based  on  x-ray  data  as  to  total  quan- 
tum number  and  origin  of  the  different  series  (Chapter  IX).  Further- 
more, the  Sommerfeld  theory  of  doublet  separations  shows  that  the 
orbits  of  each  group  have  all  the  degrees  of  ellipticity  permitted  by  the 
quantum  theory.  Thus  we  have  experimental  evidence  for  both  the 
existence  and  order  of  appearance  of  the  types  of  orbit  postulated  by 
Bohr.  Table  XLVIII  gives  in  the  lower  rows  the  x-ray  limits  corre- 
sponding to  the  different  sub-groups. 

Superficial  Atomic  Properties.  —  The  configurations  of  the  last 
bound  electrons,  shown  in  Table  XLIX,  must  determine  nearly  all  the 
chemical  and  physical  properties  of  the  elements  apart  from  x-ray 
phenomena.  It  is  seen  that  the  first  electrons  appearing  in  each  group 
have  orbits  of  azimuth  quantum  one.  It  is  impossible  to  foresee  what 
the  exact  form  of  such  an  orbit  will  be,  for  it  is  in  a  field  of  force  which 
departs  widely  from  a  Coulomb  field.  Assuming  though  that  Figure  1 
gives  the  approximate  form  and  relative  size  of  the  orbit,  we  conclude 
that  electrons  in  these  orbits  will  all  penetrate  the  entire  atom  structure 
and  at  perihelion  will  be  close  to  the  nucleus  of  charge  Ze.  This  is  in 
marked  contrast  to  other  theories,  all  of  which  have  assumed  that  the 
last  bound  electrons  move  in  a  field  of  approximately  unit  charge.  At 
aphelion  the  electrons  will  lie  far  outside  the  structure  of  previously 
bound  groups.  The  tendency  of  an  atom  to  lose  an  electron  (electro- 
positiveness)  will  depend  on  the  extension  of  the  outer  part  of  this  orbit. 
It  will  be  greatest  for  the  alkali  metals  and  will  decrease  progressively 
from  left  to  right  in  each  row  of  the  periodic  table.  The  number  of 
electrons  which  may  be  lost  (positive  valence)  correspondingly  increases. 

The  second  sub-group  formed  has  an  azimuth  number  2.  These 
orbits  will  not  extend  beyond  previously  bound  groups  and  the  electrons 
are  not  readily  lost.  On  the  contrary,  elements  preceding  the  rare 


238 


ORIGIN  OF  SPECTRA 


gases,  the  electro-negative  elements,  tend  to  take  up  electrons  to  form 
the  stable  rare  gas  configuration.  The  electro-positive  or  -negative 
properties  do  not  necessarily  imply  small  or  large  ionization  potentials. 
The  ionization  potential  is  a  measure  of  the  total  energy  of  an  orbit ;  the 
electro-positive  or  -negative  property  depends  on  the  extension  or  degree 
of  ellipticity  of  the  orbit  as  well  as  upon  the  energy.  These  properties 
are  in  strongest  contrast  in  the  second  period  (Li  to  Ne)  where  the  two 
sub-groups  differ  most  in  shape,  and  the  contrast  becomes  progressively 


.8 


Total  Quantum  Number 
5  4 


3.4     3.5      3.6       3.7       3.8      3.9      4.0      4.1       42      4.3      44      45      4.6 


Logarithm  V 


FIG.  46.     Grotrian  diagram  for  sodium  on  the  basis  of  Bohr's  new  assignment  of 

quantum  numbers. 

less  in  the  following  periods.  Thus  in  the  row  starting  with  silver  the 
two  types  of  orbits  5i  and  62  are  only  slightly  different  in  shape  and  the 
chemical  differences  are  likewise  less  pronounced. 

In  the  long  periods  where  changes  occur  in  the  sub-structure  and 
not  in  the  superficial  groups  we  have  successive  elements  with  very 
similar  physical  and  chemical  properties.  It  is  impossible  to  present 
in  this  outline  a  detailed  consideration  of  the  correspondence  between 
properties  of  elements  and  the  proposed  models.  Bohr  attempts  no 
explanation  of  the  processes  of  chemical  combination  or  crystal  forma- 
tion. 


APPENDIX  II 


239 


TABLE  L 
QUANTUM  NUMBERS  OF  SERIES  TERMS 


Series 
Term 

Sommer- 
feld 
Theory 

Bohr  Theory 

Li  arc 

Na  arc1 

Karc2 

Rb  arc3 

Cs  arc* 

n0 

nr 

na 

ttr 

na 

rcr 

rta 

Wr 

n« 

nr 

na 

nr 

1  8 

1 
1 
1 

2 
2 
2 

3 
3 
3 

4 
4 
4 

0 

1 

2 

0 
1 

2 

0 
1 
2 

0 
1 
2 

1 

1 
1 

2 
2 
2 

3 
3 
3 

4 
4 
4 

1 

2 
3 

0 
1 
2 

0 
1 
2 

0 
1 
2 

1 
1 

1 

2 
2 
2 

3 
3 
3 

4 
4 
4 

2 
3 
4 

1 
2 
3 

0 
1 
2 

0 
1 
2 

1 

1 
1 

2 
2 
2 

3 
3 
3 

4 
4 
4 

3 
4 
*5 

2 
3 
4 

1 
2 
3 

0 
1 
2 

1 
1 
1 

2 
2 
2 

3 
3 
3 

4 
4 
4 

4 
5 
6 

3 
4 
5 

2 
3 
4 

1 
2 
3 

1 
1 
1 

2 
2 
2 

3 
3 
3 

4 
4 
4 

5 
6 

7 

4 
5 
6 

3 
4 
5 

2 
3 
4 

2s  

3s 

2v. 

3p 

47?.. 

3d 

4d  

5d 

46.. 

56..   .  . 

66 

1  Similar  numbers  for  Mg  arc  and  spark. 

2  Similar  numbers  for  Cu  arc  and  Ca  and  Zn  arc  and  spark. 

3  Similar  numbers  for  Ag  arc  and  Sr  and  Cd  arc  and  spark. 

4  Similar  numbers  for  Au  arc  and  Ba  and  Hg  arc  and  spark. 

Arc  and  Spark  Spectra.  —  A  mathematical  computation  of  the  two 
orbits  of  normal  helium  and  of  the  stages  in  the  binding  of  the  second 
electron  is  being  worked  out  by  Kramers  and  Bohr.  The  solution  of 
this  very  difficult  three  body  problem  has,  we  are  assured,  already 
reached  a  stage  that  justifies  the  basic  assumptions  of  the  theory  of  non- 
hydrogen  types  of  atom.  In  heavier  elements  a  rigorous  mathematical 
solution  of  the  problem  of  the  binding  of  the  last  electron  offers  difficul- 
ties that  are  apparently  insurmountable.  The  choice  of  quantum  num- 
bers assigned  to  the  normal  state  (1  S)  by  the  Bohr  theory  makes  it 
necessary  to  reject  entirely  Sommerf eld's  theoretical  computation  of 
spectral  series  formulae.  Table  L  indicates  the  system  of  quantum 
numbers  assigned  by  Bohr  to  different  series  terms  of  elements  in  the 
first  and  second  columns  of  the  periodic  table.  For  comparison  we 
include  in  the  table  the  numbers  required  by  the  Sommerfeld  theory. 
It  is  noted  that  the  azimuth  numbers  remain  the  same  in  the  two  theo- 
ries. The  inter-orbital  transitions  involved  in  arc  spectra  of  sodium  on 
the  new  Bohr  hypothesis  are  shown  in  Figure  46.  This  should  be 


240  ORIGIN  OF  SPECTRA 

compared  with  Figure  9,  which  is  based  on  the  other  theory.  In  Figure 
46  the  double  p  terms  and  transitions  involving  combination  lines  have 
been  omitted  for  the  sake  of  simplicity.  By  our  choice  of  coordinates 
in  these  diagrams  points  and  lines  remain  identical  for  the  two  theories, 
but  total  quantum  numbers  are  entirely  different.  Hence  the  expla- 
nation of  the  features  of  Figure  9  applies,  with  the  above  noted  exception, 
to  Figure  46,  although  the  mathematical  expression  for  the  variable 
term  in  a  series  formula  would  be  entirely  different.  On  the  Bohr  theory 
total  quantum  numbers  characterizing  these  series  will  differ  for  ele- 
ments of  the  same  family,  as  shown  in  Table  L. 

Though  a  quantitative  test  of  the  Bohr  theory  of  spectra  is  im- 
possible for  heavy  elements  because  of  the  mathematics  involved,  yet 
a  comparison  of  the  relative  magnitudes  of  different  series  limits  in  the 
same  element,  and  of  corresponding  limits  in  different  elements,  offers 
a  means  of  testing  many  of  the  assumptions  as  to  the  relative  stability 
of  the  different  types  of  orbit.  For  the  elements  preceding  and  following 
the  long  periods  such  comparisons  are  particularly  interesting,  but  the 
subject  is  too  complicated  for  treatment  here. 

Conclusion.  —  Bohr's  new  hypothesis  of  atomic  structure  was 
developed  primarily  from  considerations  of  atomic  stability,  and  is  thus 
in  marked  contrast  to  other  theories  which  in  general  postulate  arbitrary 
configurations  suitable  for  the  explanation  of  a  limited  range  of  physical 
phenomena.  It  has  been  seen  that  in  the  field  of  x-ray  spectra  we  find  a 
striking  confirmation  of  Bohr's  assumptions  as  to  the  types  of  orbit 
appearing  in  the  inner  atom  structure.  It  is  only  in  the  assumed  space 
configurations  of  these  orbits  and  in  the  superficial  structure  (Table 
XLIX)  that  the  new  theory  can  be  open  to  question. 

A  space  configuration  of  electrons  is  apparently  essential  for  the 
explanation  of  chemical  and  physical  phenomena  other  than  radiation. 
The  coplanar  ring  model  assumed  in  the  past  for  the  mathematical 
computation  of  spectral  frequencies  was  adopted  because  of  its  simplicity 
and  was  generally  looked  upon  merely  as  an  approximation  to  actual 
electron  configurations.  It  has  been  applied  with  apparent  success 
to  a  wide  range  of  phenomena,  notably,  the  theoretical  derivation  of  the 
Ritz  formula  and  the  computation  of  x-ray  frequencies. 

The  new  Bohr  theory  apparently  rejects  this  model  even  as  an 
approximation,  and  the  success  of  the  theoretical  deductions  based  on 
ring  configurations  offers  the  chief  objection  to  the  acceptance  of  the 
new  viewpoint.  In  estimating  the  weight  of  this  objection  we  must 
remember  that  the  different  applications  of  the  ring  model  involve 


APPENDIX  II 


241 


many  assumptions  which  are  mutually  inconsistent.  The  new  theory 
avoids  the  artificiality  inherent  in  other  models  but  as  a  consequence 
it  lacks  the  simplicity  required  for  a  direct  mathematical  test  of  its 
validity.  Thus  we  can  foresee  that  the  quantitative  verification  of  the 
details  of  this  scheme  of  electron  distribution  may  not  be  accomplished 
in  the  near  future.  At  the  present  writing  the  entire  subject  is  in  the 
most  elementary  qualitative  stage,  but  we  are  promised  information 
of  more  quantitative  nature  from  Bohr  in  subsequent  papers. 


INDEX  OF   SUBJECTS 


Absorption  lines,  Chapter  IV,  78-108. 
of  excited  atoms,  93. 
of  ionized  atoms,  103. 
of  normal  atoms,  78. 
of  subordinate  series,  97. 
relation    to    critical    potentials, 
63. 

Absorption  phenomena,  see  x-rays. 

Affinity  for  electrons,  177,  179. 

,  of  excited  argon,  sodium  and  mer- 
cury, 106. 

,  of  excited  helium,  105. 

— ,  of  hydrogen  molecule,  76. 

Aluminum. 

— ,  K  and  L  limits  of,  204. 

— ,  raies  ultimes  of,  143. 

— ,  soft  x-rays  of,  195,  204. 

Antimony. 

— ,  raies  ultimes  of,  144. 

— ,  resonance  and  ionization  potentials 
of,  66. 

Arc  spectra,  111,  119. 

and  spark  spectra  of  elements, 

42. 

,  notation  on  basis  of  Bohr's  new 

theory,  239. 

of  alkalis,  34. 

of  heavy  atoms,  32-36. 

of  helium,  69. 

of  hydrogen,  17. 

of  metals  of  Group  I,  134. 

of  metals  of  Group  II,  125. 

Arcs. 

— ,  below  ionization  potential,  73,  77; 
115,  153. 

— ,  for  determination  of  critical  poten- 
tials, 116. 

— ,  in  nonatomic  hydrogen,  77. 

— ,   in  sodium,   of  high  luminous  effi- 
ciency, 114. 

— ,  intensity  of  emission  proportional  to 
current,  129. 

— ,  reversals,  82. 

Argon. 

— ,  M  limit,  212. 

— ,  negative  ion,  106. 

— ,  resonance  and  ionization  potentials 
of,  68.  ' 

Arsenic. 

— ,  raies  ultimes  of,  143. 


Arsenic,  resonance  and   ionization   po- 
tentials of,  66. 
Aspherical  nucleus,  28. 
Atomic  numbers  of  elements,  231. 
Atomic  structure,  15. 

,  atoms  with  many  electrons,  30,  31. 

,  Bohr's  new  theory  of,  232-241. 

,  hydrogen,  16,  74. 

,  ionized  helium,  16. 

,  normal  helium  atom,  70. 

Balmer  series,  17,  22,  25,  28. 

,  absorption  of,  97,  98. 

,  fine  structure  of,  25,  28,  37,  59,  76. 

Band  spectra,  105. 

,  continuous  band  in  iodine,  178. 

,  of  helium,  106. 

,  of  mercury  chlorides,  185. 

,  of  nitrogen,  190. 

— ,  relation  to  critical  potentials,  190. 

Barium. 

— ,  absorption  of  enhanced  lines,  103. 

— ,  development  of  spectrum,  125. 

— ,  fundamental  wave  numbers  of,  64,  85. 

— ,  raies  ultimes  of,  142. 

— ,  resonance  and  ionization  potentials 

of,  64. 

— ,  reversal  of  series  IS— mP,  83. 
— ,  series  in,  44. 

— ,  thermal  ionization,  163,  170. 
Beryllium. 
— ,  resonance  and  ionization  potentials 

of,  64. 

— ,  soft  x-rays  of,  195. 
Bismuth. 

— ,  raies  ultimes  of,  144. 
— ,  resonance  and  ionization  potentials 

of,  66. 
Boron. 

— ,  K  limit,  204. 
— ,  soft  x-rays  of,  195. 
Broadening  of  spectral  lines,  27,  91. 
Bromine. 

— ,  critical  potential  of,  67. 
— ,  electron  affinity  of,  179,  182,  186. 
— ,  heat  of  dissociation  of,  182,  186. 
— ,  K  absorption  band,  196. 


Cadmium. 

— ,  absorption  of  X  3260  and  X  2288  A,  81. 


243 


244 


INDEX  OF  SUBJECTS 


Cadmium,  development  of  spectrum,  125. 
— ,  fundamental  wave  numbers  of,  64,  85. 
— ,  raies  ultimes  of,  142. 
— ,  resonance  and  ionization  potentials 

of,  64. 

— ,  series  in,  44. 
— ,  single  line  spectrum,  124. 
— ,  thermal  ionization,  163. 
— ,  two  line  spectrum,  124. 
Caesium. 

— ,  absorption  lines  of,  80. 
— ,  development  of  spectrum,  134. 
— ,  fundamental  wave  numbers  of,  62. 
— ,  photo-electric  effect  in  vapor,  217. 
— ,  possibility  of  higher  resonance  po- 
tentials, 127. 
— ,  raies  ultimes  of,  142. 
— ,  resonance  and  ionization  potentials 

of,  62. 

— ,  reversal  of  subordinate  series  of,  108. 
— ,  reversed  lines,  82. 
— ,  series  in,  44. 

— ,  single-doublet  and  arc  spectra,  129. 
— ,  thermal  ionization  of,  163. 
Calcium. 
— ,   absorption  of  X  4227  A  in  furnace 

spectra,  82. 

— ,  development  of  spectrum,  125. 
— ,  flame  spectrum,  166. 
— ,  fundamental  wave  numbers  of,  64, 84. 
— ,  in  solar  spectrum,  171,  172. 
— ,  in  stellar  spectra,  174. 
— ,  raies  ultimes  of,  142. 
— ,  resonance  and  ionization  potentials 

of,  64. 

— ,  reversal  of  enhanced  lines,  103. 
— ,  reversal  of  series  1  S-mP,  83. 
— ,  series  in,  44. 

— ,  thermal  ionization  of,  160,  163,  170. 
Carbon. 
— ,  ionization  and  resonance  potentials 

of  compounds  of,  188. 
— ,  K  limit,  204. 
— ,  raies  ultimes  of,  143. 
— ,  soft  x-rays  of,  195. 
Chlorine. 

— ,  critical  potentials  of,  67. 
— ,  electron  affinity  of,  179,  182,  186. 
— ,  heat  of  dissociation  of,  182,  186. 
— ,  soft  x-rays  of,  195. 
Chromium. 

— ,  in  solar  spectrum,  172. 
— ,  raies  ultimes  of,  144. 
Cobalt. 

— ,  in  solar  spectrum,  172. 
— ,  raies  ultimes  of,  144. 
Columbium. 
— ,  raies  ultimes  of,  143. 
Copper. 
— ,  development  of  spectrum  of,  134. 


Copper,  fundamental  wave  numbers  of 

62. 
— ,  ionization  and  resonance  potentials 

of,  62. 

—  raies  ultimes  of,  142. 

—  reversal  of  X  3248  and  X  3275  A,  83. 

—  series  in,  44. 

—  soft  x-rays  of,  195. 

—  thermal  ionization  of,  163. 
Cumulative  ionization,  148-156. 

Data,  numerical,  227-231. 
Displacement  law  for  spectra,  42. 
Dissociation. 

—  of  halogens,  182. 

—  of  hydrogen,  75,  76. 
Doppler-Fizeau  effect,  27,  88,  91. 

e/m,  value  of,  18. 

Emission  lines,  Chapter  V,  109-147. 

,  metajs  of  Group  I,  127. 

,  metals  of  Group  II,  118. 

,  rare  gases,  133. 

Energy  diagrams. 

,  Grotrian  diagram;  for  hydrogen, 

57;  sodium,  58,  238. 

,  helium,  70. 

,  hydrogen,  52. 

,  ionized  magnesium,  56. 

,  magnesium,  54. 

,  mercury,  101. 

— ,  sodium,  53,  58. 

,  sodium  (Bohr's  new  theory),  238. 

,  tungsten  (x-rays),  206. 

— ,  uranium  (x-rays),  208. 
Enhanced  spectra,  113.     (See  also  Spark 

spectra.) 

constants  in  series  formulae,  40. 

of  metals  of  Group  I,  134. 

—  of  metals  of  Group  II,  119,  125. 

,  relation  between  a*  and  a,  41. 

,  relation  between  1  ©  and  1  S,  124. 

,  series  notation  for,  41. 

Excited  atoms,  79,  90,  150. 

,  electron  affinity  of,  105. 

,  life  of,  92,  93. 

,  line  absorption  spectra  of,  93-108. 

,  produced  thermally,  157-176. 

Fine  structure,  25,  26,  27. 

,  doublets  and  triplets,  37. 

,  L-doublet  separation,  49. 

of  Balmer  lines,  37. 

of  x-ray  spectra,  209-213. 

,    relation    of    L-doublets    to    arc 

spectrum  of  neon,  136. 
Flame  spectra,  82,  84,  165. 
,  suppression  of  sodium  lines  with 

excess  of  chlorine,  184. 
Fluorescence,  90,  107. 


INDEX  OF  SUBJECTS 


245 


Fluorescence,  of  mercury,  104,  107. 
—  of  x-radiation,  197. 

Gallium. 

— ,  raies  ultimes  of,  143. 

Germanium. 

— ,  raies  ultimes  of,  143. 

Gold. 

— ,  development  of  spectrum  of,  134. 

— ,  fundamental  wave  numbers  of,  62. 

— ,  N  -limit,  204. 

— ,  raies  ultimes  of,  142. 

— ,  resonance  and  ionization  potentials 

of,  62. 

— ,  reversal  of  X  2428  A,  83. 
— ,  series  in,  44,  83. 
— ,  thermal  ionization  of,  163. 
Grating  energy,  179. 

of  alkalf  halides'  182. 

of  ZnS,  183. 

h,     determinations    of,    involving    line 

spectra,  223-226. 
Helium. 

— ,  absorption  of  excited  atom,  103. 
— ,  compounds  of,  74,  106. 
— ,  development  of  spectrum  of,  133. 
— ,  electron  affinity  of,  105. 
— ,  energy  diagram,  70. 
" — ,  fine  structure  of  ionized,  28. 
— ,  in  stellar  spectra,  174. 
— ,  K  series,  199. 
— ,  metastable,  73. 
— ,  new  ultra-violet  lines,  77. 
— ,  ortho-  and  par-helium,  72. 
— ,  photo-electric  effect  in,  222. 
— ,  resonance  and  ionization  potentials 

of,  68,  73. 

— ,  resonance  radiation  of,  90. 
— ,  series  in  ionized  atom,  17. 
— ,  series  in  neutral  atom,  69-74. 
— ,  structure  of  ionized  atom,  16. 
— ,  the  normal  atom,  69. 
Hydrogen. 
— ,  arcs  in,  77. 

— ,  continuous  absorption  in,  222. 
— ,  doublet  separation,  29. 
— ,  electron  affinity  of  molecule,  76. 
— ,  energy  diagrams,  52,  57. 
— ,  halides,  ionization  potentials  of,  186, 

188. 

— ,  in  solar  spectrum,  171. 
— ,  in  stellar  spectra,  174. 
— ,  ionization  potential  of  HCN,  188; 

of  water  vapor,  188. 
— ,  life  of  excited  atom,  96. 
— ,  molecule,  74-77. 
— ,  ratio  of  mass  of  nucleus  and  atom  to 

mass  of  electron,  18. 


Hydrogen,  resonance  and  ionization  po- 
tentials of,  68. 

—  series  in,  17,  22. 

—  structure  of  atom,  16. 

—  sulphide,  ionization  of,  187. 

—  thermal  ionization  of,  161,  163. 

—  work  of  dissociation  of,  75,  76. 

Impact  damping,  92. 
Indium. 

—  ,  raies  ultimes  of,  143. 
Iodine. 

—  electron  affinity,  179,  182,  186. 

—  emission  from  recombination,  190. 

—  emission  spectrum,  178. 

—  heat  of  dissociation,  182,  186. 

—  resonance  and  ionization  potentials 
of,  67. 

Ionization.     (See  also  Ionization  poten- 
tials.) 

—  by  photo-electric  action,  154,  217. 

—  by  photo-impact,  148. 

—  by  successive  impact,  148. 
Ionization  potentials. 

--  ,  determination  of  h,  225. 
--  ,  higher,  and  x-ray  limits,  196. 
--  ,  of  compounds,  179-191. 
--  ,  of  elements,  60-68. 
Iridium. 

—  ,  raies  ultimes  of,  144. 
Iron. 

—  ,  in  solar  spectrum,  172. 

—  ,  raies  ultimes  of,  144. 

—  ,  soft  x-rays,  195. 

Lead. 

—  ,  raies  ultimes  of,  143. 

—  ,  resonance  and  ionization  potentials 
of,  65. 

Life  of  excited  atoms,  92,  105. 
--  ,  measurement  of,  93. 
Limits  of  series. 
--  arc  spectra,  125,  134. 
--  enhanced  spectra,  118,  125,  134. 
--  significance  of  x-ray,  209. 
--  spectral,  45;  determining  ioniza- 
tion, 61,  111,  112. 

x-ray,  46,  195,  198,  201,  203,  204. 


—  ,  absorption  lines  of,  80. 

—  ,  development  of  spectrum  of,  134. 

—  ,  doubly  ionized,  16,  42;  series  in,  44. 

—  ,  flame  spectrum,  166. 

—  ,  fundamental  wave  numbers  of,  62. 

r,  ionization  and  resonance  potentials 
of,  62. 

—  ,  raies  ultimes  of,  142. 

—  ,  reversed  lines,  82. 

—  ,  thermal  excitation  of,  168. 

—  ,  thermal  ionization  of,  163. 


246 


INDEX  OF  SUBJECTS 


Long  lines,  141. 

Lyman  series,  17,  25,  59,  75. 

Magnesium. 

— ,  absorption  of  enhanced  lines,  103 

— ,  absorption  of  X  2852  and  X  2026  A,  82 

— ,  complete  arc  spectrum,  121 

— ,  complete  enhanced  spectrum,  122 

— ,  development  of  spectrum,  118,  125. 

— ,  energy  diagrams,  54,  56. 

— ,  fundamental  wave  numbers  of  64  84 

— ,  in  stellar  spectra,  174. 

— ,  raies  ultimes  of,  142. 

— ,  resonance  and  ionization  potentials 

— ,  series  in,  44. 

— ,  single  line  spectrum,  118. 

— ,  single  line  spectrum  of  ionized   122 

— ,  soft  x-rays,  195,  204. 

— ,  thermal  ionization,  163. 

— ,  two  line  spectrum,  121. 

Manganese. 

— ,  in  solar  spectrum,  172. 

— ,  raies  ultimes  of,  144. 

— ,  1  S  and  ionization  potential,  67 

Mass. 

— ,  correction  for  finite,  of  nucleus,  17. 

— ,  of  hydrogen  nucleus,  15. 

— ,  ratio  of,  hydrogen  nucleus  and  atom 

to  mass  of  electron,  18. 
Mercury. 
— ,  absorption  coefficient  of  vapor  for 

resonance  radiation,  89. 
— ,  absorption  of  subordinate  series,  99, 
— ,  absorption  of  X  1849  and  X  2537  A. 

81,  88,  89,  100,  108. 
— ,  development  of  spectrum  of,  125 
— ,  energy  diagram,  101. 
— ,  fluorescence,  104. 
— ,  fundamental  wave  numbers  of,  64,  85 
— ,  higher  critical  potentials,  137. 
— ,  ionization  potential  of  HgCl2,  188. 
— ,  metastable  form  of,  102, 106, 108  140 
— ,  molecule,  106. 
— ,  raies  ultimes  of,  143. 
— ,  resonance  and  ionization  potentials 

of,  64. 
— ,  resonance  potential  by  probe  wire 

measurements,  114. 
— ,  resonance  radiation,  86-89. 
— ,  series  in,  44. 
— ,  single  line  spectrum,  124. 
— ,  thermal  ionization,  163. 
Molybdenum. 
— ,  raies  ultimes  of,  144. 
— ,  soft  x-rays,  195. 

Neon. 

— ,  development  of  spectrum,  136. 


Neon,  L  series,  200. 

,  resonance  and  ionization  potentials 

of,  68. 
Nickel. 

— ,  in  solar  spectrum,  172. 
— ,  raies  ultimes  of,  144. 
— -,  soft  x-rays,  195. 
Nitrogen. 

— ,  complex  critical  potentials,  190. 
— ,  excitation  of  band  spectra,  190. 
— ,  resonance  and  ionization  potentials 

of,  66. 

— ,  soft  x-rays,  195. 
Nuclear  defect  of  a  ring  of  electrons,  37, 

227. 
Numerical  magnitudes,  228. 

Orbits,  15. 

— ,  application    of    general    quantizing 

equation,  21. 
— ,  circular,    of   hydrogen    and    ionized 

helium,  16,  23. 
— ,  elliptical,  19,  21. 
— ,  modifications    arising    in    relativity 

considerations,  24. 
— ,  of  helium,  70. 
Oxygen. 

— ,  resonance  and  ionization  potentials 

of,  67. 
— ,  soft  x-rays,  195. 

Palladium. 

— ,  raies  ultimes  of,  144. 

Paschen  series,  17,  25,  59. 

Periodic  table,  30,  231. 

Phosphorus. 

— ,  raies  ultimes  of,  143. 

— ,  resonance  and  xonization  potentials 
of,  66. 

— ,  soft  x-rays,  195. 

Photo-electric  effect  in  vapors,  216-222. 

and  ionization,  217.  - — 

in  caesium  vapor,  217. 

Photo-electric  ionization,  148. 

Platinum. 

— ,  raies  ultimes  of,  144. 

Potassium. 

— ,  absorption  lines  of,  80. 

— ,  continuous  absorption,  221. 

— ,  development  of  spectrum  of,  134. 

— ,  fundamental  wave  numbers  of,  62. 

— ,  heat  of  sublimation  of,  182. 

— ,  ionization  and  resonance  potentials 

of,  62. 

— ,  raies  ultimes  of,  142. 
— ,  reversed  lines,  82. 
— ,  reversal  of  subordinate  series  of,  108 
— ,  series  in,  44. 

— ,  single  line,  arc,  and  enhanced  spec- 
tra, 129. 


INDEX  OF  SUBJECTS 


247 


Potassium,  thermal  ionization  of,  163. 
— ,  soft  x-rays,  195. 

Quantum  numbers,  16. 

,  definition  of  azimuthal  and  radial, 

21. 

-,  determination  of,  20. 

,  for  alkalis,  34. 

,  for  hydrogen  series,  17. 

,  of  series  terms  on  basis  of  Bohr's 

new  theory,  239. 

,  of  x-ray  limits,  210. 

Quantum  theory,  15-50. 

Radium. 

— ,  development  of  spectrum  of,  125. 
— ,  fundamental  wave  numbers  of,  64. 
— ,  resonance  and  ionization  potentials 

of,  64. 

— ,  series  in,  44. 
Raies  ultimes,  141. 

of  the  elements  (table),  142. 

Relativity,  of  mass,  24. 

hydrogen  doublet,  29. 

L-doublet,  49. 

Resonance  potentials. 

,  determination  of  h,  225. 

,  of  compounds,  188. 

,  of  elements,  60-68. 

Resonance  radiation,  86,  147. 

Retarded  potential,  28. 

Reversed  lines,  82. 

Rhodium. 

— ,  raies  ultimes  of,  144. 

Ritz  equation,  32,  43. 

Rubidium. 

— ,  absorption  lines  of,  80. 

— ,  development  of  spectrum  of,  134. 

— ,  fundamental  wave  numbers  of,  62. 

— ,  raies  ultimes  of,  142. 

— ,  resonance  and  ionization  potentials 

of,  62. 

— ,  reversal  of  subordinate  series,  108. 
— ,  reversed  lines,  82. 
— ,  series  in,  44. 
— ,  thermal  ionization  of,  163. 
Ruthenium. 

— ,  raies  ultimes  of,  144. 
Rydberg  number,  N,  N^,  Nu,  Nse,  17, 

18,  19. 
j  determination  of  h,  224. 

Scandium. 

— ,  in  solar  spectrum,  172. 
— ,  raies  ultimes  of,  143. 
Selection,  principle  of,  26,  28,  35,  72,  86, 
87,  88,  121,  140. 

m  absorption,  78. 

in  x-rays,  212. 


Selection,  principle  of,  representation  in 
Grotrian  diagrams,  59. 

,  ls-3d  in  sodium  and  potassium, 

130. 

Selenium. 
— ,  resonance  and  ionization  potentials 

of,  67. 

Series.     (See  x-rays.) 
— ,  absorption,  Chapter  IV. 
— ,  emission,  Chapter  V. 
— ,  graphic  representation  of,  51-59. 
— ,  in  alkalis,  34. 
— ,  in  heavy  atoms,  32-36. 
— ,  in  helium,  17. 
— ,  in  hydrogen,  17. 

— ,  lines    correlated    with    temperature, 
169. 

— ,  notation  and  formulae,  43-46. 

— ,  notation    on   basis   of   Bohr's   new 
theory,  239. 

— ,  reversals,  82. 

Silicon. 

— ,  raies  ultimes  of,  143. 

— ,  soft  x-rays,  195. 

Silver. 

— ,  development  of  spectrum,  134. 

— ,  fundamental  wave  numbers  of,  62. 

— ,  K  absorption  band,  196. 

— ,  raies  ultimes  of,  142. 

— ,  resonance  and  ionization  potentials 
of,  62. 

— ,  series  in,  44. 

— ,  thermal  ionization  of,  163. 

Size. 

—  of  hydrogen  nucleus,  15. 

—  radius  of  hydrogen  atom,  38. 
Sodium. 

— ,  absorption  of,  79. 

— ,  continuous  absorption  of,  219,  220. 

— ,  energy  diagrams,  53,  58. 

— ,  development  of  spectra  of,  129,  134. 

— .  energy  diagram  (Bohr's  new  theory), 

238. 

— ,  flame  spectrum,  166. 
— ,  fundamental  wave  numbers  of,  62,  87. 
— ,  in  solar  spectrum,  171,  172. 
— ,  ionization  and  resonance  potentials 

of,  62. 

— ,  metastable  ion,  130. 
— ,  negative  ion,  106. 
— ,  raies  ultimes  of,  142. 
— ,  resonance  radiation,  86. 
— ,  reversal  of  subordinate  series,  97, 108. 
— ,  reversed  lines,  82. 
— ,  series  in,  44. 
— ,  single  line  spectrum,  129. 
— ,  soft  x-rays,  195,  204. 
— ,  subordinate  series  terms   of  higher 

order,  117. 
— ,  thermal  excitation,  165. 


248 


INDEX  OF  SUBJECTS 


Sodium,  thermal  ionization,  163. 
Solar  spectra,  169,  170. 
Spark  spectra,  39,  112. 

—  — ,  alkali  earths,  118. 
,  helium,  17,  28. 

,  notation  on  basis  of  Bohr's  new 

theory,  239. 

Spectroscopic  analysis,  141. 

Spectroscopic  tables,  43. 

Stark  effect,  7,  27,  29. 

Stellar. 

— ,  continuous  band  absorption  in  spec- 
tra, 222. 

—  spectra,  169,  172,  174,  176. 
—  temperatures,  173,  176. 

Stokes'  law,  102. 

Strontium. 

— ,  absorption  of  enhanced  lines,  103. 

— ,  development  of  spectrum,  125. 

— ,  flame  spectrum,  166. 

— ,  fundamental  wave  numbers  of,  64,  85. 

— ,  in  solar  spectrum,  172. 

— ,  raies  ultimes  of,  142. 

— ,  resonance  and  ionization  potentials 

of,  64. 

— ,  reversal  of  series  1  S-mP,  83. 
— ,  series  in,  44. 

— ,  thermal  ionization  of,  163,  170. 
Sulphur. 

— ,  electron  affinity  of,  179,  183. 
— ,  heat  of  dissociation  of,  183. 
— ,  heat  of  sublimation  of,  183. 
— ,  resonance  and  ionization  potentials 

of,  67. 
— ,  soft  x-rays,  195. 

Tantalum. 

— ,  raies  ultimes  of,  143. 

Tellurium. 

— ,  raies  ultimes  of,  144. 

— ,  resonance  and  ionization  potentials 
of,  67. 

Thallium. 

— ,  absorption  of  vapor,  83. 

— ,  excitation  of  lines  of,  in  mixtures  of 
Tl  and  Hg,  108. 

— ,  raies  ultimes  of,  143. 

— •,  resonance  and  ionization  potentials 
of,  65. 

— ,  reversals  in  arc,  83. 

Thermal  excitation,  157-176. 

Thermochemical  relations,  177-191. 

Thermodynamics  of  excitation  and  ioni- 
zation, 157-176. 

Tin. 

— ,  raies  ultimes  of,  143. 

Titanium. 

— ,  in  solar  spectrum,  172. 

— ,  raies  ultimes  of,  143. 

— ,  soft  x-rays,  195. 


Tungsten. 

— ,  complete  x-ray  spectra  of,  205-207. 

— ,  energy  diagram  (x-rays),  206. 

— ,  raies  ultimes  of,  144. 

— ,  soft  x-rays,  195. 

Ultra-violet,  continuous  source  of,  81. 

Uranium. 

— ,  energy  levels  (x-rays),  208. 

— ,  K  limit,  199. 

Vanadium. 

— ,  in  solar  spectrum,  172. 
— ,  raies  ultimes  of,  143. 
Velocities  of  electrons,  ions  and  mole- 
cules, 229. 

Wave  number,  definition  of,  17, 

X-rays,  46-;50,  192-215. 

— ,  absorption  limits  (table),  204. 

— ,  absorption  phenomena,  196. 

— ,  combination  principle,  204. 

— ,  critical  potentials  for  excitation,  193. 

— ,  determination  of  h,  223. 

— ,  diagram  of  K  limits,  201. 

— ,  diagram  of  L  and  M  limits,  203. 

— ,  diagram  of  x-ray  limits  of  elements, 

198. 

— ,  emission  lines,  204. 
— ,  interpretation  by  Bohr's  new  theory, 

237. 

— ,  N  series,  215. 

— ,  relation  to  arc  spectrum  of  neon,  136. 
— ,  significance  of  limits,  209. 
— ,  simple  series  nomenclature,  47. 
— ,  spark  lines  accompanying,  134. 
— ,  structure  of  band  absorption,  200. 
— ,  table  of  soft  x-rays,  195. 
— ,  values  of  v/N,  48. 

Yttrium. 

— ,  raies  ultimes  of,  143. 

Zeeman  effect,  7,  29. 

Zinc. 

— ,  absorption  of  X  3076  and  X  2139  A,  82. 

— ,  development  of  spectrum  of,  125. 

— ,  fundamental  wave  numbers  of,  64,  84. 

— ,  heat  of  sublimation  of,  183. 

— ,  ionization   potentials   of  ZnCl2  and 

zinc  ethyl,  187,  188. 
— ,  raies  ultimes  of,  142. 
—  resonance  and  ionization    potentials 

of,  64. 

— ,  series  in,  44. 

— ,  single  line  and  two  line  spectra,  124. 
— ,  thermal  ionization  of,  163. 
Zirconium. 
— ,  raies  ultimes  of,  143. 


INDEX  OF  AUTHORS 


Adams,  Edwin  Plimpton,  50. 
Anderson,  J.  A.,  72. 

Bazzoni,  C.  B.,  195,  213,  214. 

Bergengren,  J.,  215. 

Be  van,  P.  V.,  80. 

van  der  Bijl,  H.  J.,  155. 

Birge,  R.  T.,  19,  190,  223. 

Bloch,  E.,  190. 

Bloch,  Leon,  190. 

Bodenstein,  M.,  186. 

Bohr,  Nils,  7,  16,  26,  28,  30,  31,  35,  36, 

50,  69,  71,  74,  77,  130,  186,  214,  215, 

232-241. 

Bormanri,  Elisabeth,  183,  186. 
Born,  Max,  179,  183,  186. 
Boucher,  P.  E.,  188. 
Brackett,  F.  S.,  135. 
Bragg,  W.  H.,  204. 
Brandt,  Erich,  66,  190. 
de  Broglie,  M.,  192  B,  197,  199,  214,  215. 
BuddeJ  Hans,  183. 

Cario,  108. 

Catalan,  M.,  67. 

Child,  C.  D.,  156. 

Chi-Sun-Yeh,  223. 

Clark,  H.,  224. 

Coblentz,  W.  W.,  172,  173. 

Compton,  K.   T.,  8,  67,  68,   135,   148, 

151,  153,  168,  189. 
Coster,  D.,  205,  215. 
Curtiss,  R.  H.,  97. 

Darwin,  C.  G.,  28. 

Dauvillier,  A.,  215. 

Davies,  A.  C.,  67,  68,  75,  95,  136,  222. 

Davis,  Bergen,  137. 

Dempster,  A.  J.,  96. 

Dixon,  A.  A.,  67. 

Dolejsek,  V.,  215. 

Duane,  William,  197,  199,  205,  212,  215, 

223,  224. 

Duffenback,  O.  S.,  77. 
Dunoyer,  L.,  87. 
Dunz,  Berthold,  43. 
Dushman,  Saul,  26. 


Edwards,  E.,  81,  137. 
Einsporn,  E.,  120,  137. 
Einstein,  A.,  197. 


Fairchild,  C.  O.,  99. 

Fajans,  K.,  182. 

Foote,  Paul  D.,  36,  60-68,  75,  76,  81, 

108,  116,  118,  124,  128,  129,  130,  132, 

186,  187,  188,  190,  194,  195,  200,  201, 

204,  213,  214,  217,  225. 
Fortrat,  R.,  79. 
Fowler,  A.,  39,  43-46,  50,  64,  65,  66,  67, 

69,  136. 
Franck,  J.,  7,  68,  71,  73,  74,  77,  90,  91, 

92,  105,  106,  108,  120,  124,  133,  137, 

177,  183,  186. 

Fricke,  Hugo,  72,  199,  200,  204,  215. 
Fuchtbauer,  Chr.,  100,  155,  217. 

Gehrcke,  E.,  28. 

Gerlach,  W.,  77,  183. 

Gossling,  B.  G.,  188. 

Goucher,  F.  S.,  137. 

de  Gramont,  A.,  141. 

Grotrian,  Walter,  59,  105,  106,  114,  136, 

138,  239. 
Guthrie,  D.  V.,  81,  83. 

Harrison,  G.  R.,  80,  219. 

Hartley,  W.  N.,  141. 

Hartmann,  J.,  222. 

Henderson,  J.  P.,  124. 

Hertz,  G.,  124,  199,  215. 

Hicks,  W.  M.,  45. 

Hjalmar,  E.,  215. 

Holden,  W.  H.,  230. 

Holtsmark,  J.,  220. 

Holweck,  F.,  202,  204,  215,  224. 

Horton,  Frank,  67,  68,  75,  95,  136,  222. 

Howe,  H.  E.,  81. 

Hoyt,  F.  C.,  205,  214. 

Huggins,  William,  222. 

Hughes,  A.  L.,  66,  67,  68,  77,  195,  196, 

214,  216. 
Hulburt,  E.,  81. 
Hull,  A.  W.,  224. 

Ireton,  H.  J.  C.,  124. 
Jolly,  H.  L.  P.,  129. 

Kannenstine,  F.  M.,  73. 
Kayser,  H.,  97,  103. 
Kemble,  E.  C.,  70,  74. 
Kiess,  C.  C.,  141. 


249 


250 


INDEX  OF  AUTHORS 


King,  A.  S.,  82,  103,  108,  169,  170. 

Klein,  O.,  108. 

Knipping,  P.,  68,  71,  73,  133,  186,  188. 

Konen,  H.  M.,  43. 

Kossel,  W.,  42,  200,  205,  215. 

Kramers,  H.  A.,  29,  239. 

Kunz,  J.,  217. 

Kurth,  E.  H.,  76,  194,  195,  204,  213,  214. 

Ladenburg,  R.,  99,  223. 

Lande,  A.,  71. 

Langmuir,  Irving,  30,  75,  152,  186. 

Lau,  F.,  28. 

Lenz,  W.,  106,  190. 

Lewis,  E.  P.,  81. 

Lewis,  G.  N.,  30. 

Lilly,  E.  G.,  135. 

Lindh,  A.  E.,  215. 

Lockyer,  Norman,  141. 

Lohmeyer,  J.,  185. 

Lorenser,  E.  D.,  43. 

Lorentz,  H.  A.,  91,  92. 

Lowe,  P.,  28. 

Lyman,  Theodore,  72,  77. 

McLennan,  J.  C.,  8,  28,  77,  81,  82,  83, 

124,  137,  165. 
Mees,  C.  E.  K,  129. 
Merton,  T.  R.,  28. 
Meggers,  W.  F.,  8,  36,  81,  82,  85,  97, 108, 

116,  118,  124,  128,  129,  130,  132,  141, 

142,  166,  190. 
Metcalfe,  E.  P.,  99. 
Mie,  Gustav,  96. 
Millikan,  R.  A.,  204,  213,  215. 
Milne,  E.  A.,  171. 
Mixter,  W.  G.,  183. 
Mohler,  F.  L.,  36,  62-68,  75,  76,  81,  87, 

108,  116,  118,  124,  129,  130,  132,  186, 

187,  188,  190,  194,  195,  200,  201,  204, 

213,  214,  217,  235. 
Moseley,  J.  H.,  192,  204. 
Munch,  W.,  172. 

Nagaoka,  H.,  27. 
Noyes,  A.  A.,  8. 
Noyes,  W.  A.,  8. 

Oldenberg,  O.,  28. 

Page,  Leigh,  50. 

Palmer,  H.  H.,  223. 

Paschen,  F.,  7,  18,  19,  28,  29,  30,  43,  65, 

73,  103,  136,  225. 
Peters,  C.  G.,  85. 
Phillips,  F.  S.,  104. 
Pier,  M.,  186. 
Planck,  M.,  16,  24,  223. 
Pollitzer,  F.,  183. 


Raleigh,  Lord,  24,  91. 

Randall,  H.  M.,  65. 

Rawlinson,  W.  F.,  214. 

Reiche,  F.,  71,  73,  74. 

Rice,  M.,  224. 

Richardson,  O.  W.,  195,  213,  214. 

Robinson,  H.,  214. 

Ross,  P.  A.,  214. 

Rosseland,  S.,  108. 

Ruark,  Arthur  E.,  8,  28,  230. 

Rubinowicz,  A.,  26,  36,  212. 

Russell,  H.  N.,  171,  172,  175. 

Rutherford,  Ernest,  15,  197,  214. 

Saha,  M.  N.,  67,  159,  171,  172,  173,  175. 

Saunders,  F.  A.,  84,  85. 

Scheiner,  J.,  172,  173. 

Siegbahn,  M.,    205,  208  A,  208  B,215. 

Silberstein,  Ludwick,  28,  50. 

Skinner,  C.  A.,  8. 

Smekal,  A.,  205,  215. 

Smyth,  H.  D.,  67,  189. 

Sommerfeld,  A.,  7,  20,  24,  26,  28,  32,  36, 

40,  42,  49,  50,  62,  120,  140,  190,  209, 

210,  215. 
Starck,  G.,  186. 
Stark,  J.,  153. 
Stead,  G.,  188. 
Stenstrom,  W.,  199,  200,  215. 
Steubing,  W.,  178. 
Stimson,  F.  J.,  141. 
Stratton,  S.  W.,  8. 
Strutt,  R.  J.,  86. 

Tate,  J.  T.,  60,  63. 
Thomson,  A.,  165. 
Tolman,  R.  C.,  8,  157,  158,  164. 

Udden,  A.  D.,  67. 

Van  Vleck,  J.  H.,  74. 
Venkatesachar,  B.,  99. 
Vinal,  G.  W.,  18. 

Waidner,  C.  W.,  8. 

Webster,  D.  L.,  194,  214,  244. 

Wentzel,  G.,  205,  212,  215. 

Wien,  W.,  96. 

Williams,  E.  H.,  217. 

Wilsing,  J.,  172,  173. 

Wilson,  W.,  20. 

Wood,  R.  W.,  79,  80,  81,  83,  86,  87,  88, 

89,  96,  98,  105,  107,  152,  168,  190,  218, 

219. 
Wooten,  B.  A.,  224. 

Young,  J.  F.  T.,  83. 
Zahn,  H.;  98,  166,  167,  168. 


re  i i 137 


C  <{& 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


|^K] 

• 


9BHHHH 


